Abstract We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity.
{"title":"Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent","authors":"Yanhua Deng, Zhong Tan, M. Xie","doi":"10.1515/anona-2022-0306","DOIUrl":"https://doi.org/10.1515/anona-2022-0306","url":null,"abstract":"Abstract We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43509178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we study the following Klein-Gordon-Maxwell system: − Δ u − ( 2 ω + ϕ ) ϕ u = g ( u ) , in R 3 , Δ ϕ = ( ω + ϕ ) u 2 , in R 3 , left{phantom{rule[-1.25em]{}{0ex}}begin{array}{l}-Delta u-left(2omega +phi )phi u=gleft(u),hspace{1.0em}{rm{in}}hspace{1em}{{mathbb{R}}}^{3},hspace{1.0em} Delta phi =left(omega +phi ){u}^{2},hspace{1.0em}{rm{in}}hspace{1em}{{mathbb{R}}}^{3},hspace{1.0em}end{array}right. where ω omega is a constant that stands for the phase; u u and ϕ phi are unknowns and g g satisfies the Berestycki-Lions condition [Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313–345; Nonlinear scalar field equations. II. Existence of infinitelymany solutions, Arch. Rational Mech. Anal. 82 (1983), 347–375]. The Klein-Gordon-Maxwell system is a model describing solitary waves for the nonlinear Klein-Gordon equation interacting with an electromagnetic field. By using variational methods and some analysis techniques, the existence of positive solution and multiple solutions can be obtained. Moreover, we study the properties of decay estimates and asymptotic behavior for the positive solution.
{"title":"Existence of nontrivial solutions for the Klein-Gordon-Maxwell system with Berestycki-Lions conditions","authors":"Xiao-Qi Liu, Gui-Dong Li, Chunquan Tang","doi":"10.1515/anona-2022-0294","DOIUrl":"https://doi.org/10.1515/anona-2022-0294","url":null,"abstract":"Abstract In this article, we study the following Klein-Gordon-Maxwell system: − Δ u − ( 2 ω + ϕ ) ϕ u = g ( u ) , in R 3 , Δ ϕ = ( ω + ϕ ) u 2 , in R 3 , left{phantom{rule[-1.25em]{}{0ex}}begin{array}{l}-Delta u-left(2omega +phi )phi u=gleft(u),hspace{1.0em}{rm{in}}hspace{1em}{{mathbb{R}}}^{3},hspace{1.0em} Delta phi =left(omega +phi ){u}^{2},hspace{1.0em}{rm{in}}hspace{1em}{{mathbb{R}}}^{3},hspace{1.0em}end{array}right. where ω omega is a constant that stands for the phase; u u and ϕ phi are unknowns and g g satisfies the Berestycki-Lions condition [Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313–345; Nonlinear scalar field equations. II. Existence of infinitelymany solutions, Arch. Rational Mech. Anal. 82 (1983), 347–375]. The Klein-Gordon-Maxwell system is a model describing solitary waves for the nonlinear Klein-Gordon equation interacting with an electromagnetic field. By using variational methods and some analysis techniques, the existence of positive solution and multiple solutions can be obtained. Moreover, we study the properties of decay estimates and asymptotic behavior for the positive solution.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49360375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.
{"title":"Incompressible limit for compressible viscoelastic flows with large velocity","authors":"Xianpeng Hu, Yaobin Ou, Dehua Wang, Lu Yang","doi":"10.1515/anona-2022-0324","DOIUrl":"https://doi.org/10.1515/anona-2022-0324","url":null,"abstract":"Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42191352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, under some weaker assumptions on a > 0 agt 0 and f f , the authors aim to study the existence of nontrivial radial solutions and nonexistence of nontrivial solutions for the following Schrödinger-Poisson system with zero mass potential − Δ u + ϕ u = − a ∣ u ∣ p − 2 u + f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. where p ∈ 2 , 12 5 pin left(2,frac{12}{5}right) . In particular, as a corollary for the following system: − Δ u + ϕ u = − ∣ u ∣ p − 2 u + ∣ u ∣ q − 2 u , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. a sufficient and necessary condition is obtained on the existence of nontrivial radial solutions.
摘要本文在> 0 a gt 0和f f的一些较弱的假设下，研究了以下具有零质量势能的Schrödinger-Poisson系统- Δ u + φ u = - a∣u∣p - 2 u + f (u)， x∈R 3， - Δ φ = u 2, x∈R 3, left ｛begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right的非平凡径向解的存在性和非平凡解的不存在性。式中p∈2,125 p inleft (2, frac{12}{5}right)。特别地，作为以下系统的推论:−Δ u + φ u =−∣u∣p−2 u +∣u∣q−2 u, x∈R 3，−Δ φ = u 2, x∈R 3, left ｛begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right。得到了非平凡径向解存在的一个充要条件。
{"title":"Existence and nonexistence of nontrivial solutions for the Schrödinger-Poisson system with zero mass potential","authors":"Xiaoping Wang, Fulai Chen, Fangfang Liao","doi":"10.1515/anona-2022-0319","DOIUrl":"https://doi.org/10.1515/anona-2022-0319","url":null,"abstract":"Abstract In this article, under some weaker assumptions on a > 0 agt 0 and f f , the authors aim to study the existence of nontrivial radial solutions and nonexistence of nontrivial solutions for the following Schrödinger-Poisson system with zero mass potential − Δ u + ϕ u = − a ∣ u ∣ p − 2 u + f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. where p ∈ 2 , 12 5 pin left(2,frac{12}{5}right) . In particular, as a corollary for the following system: − Δ u + ϕ u = − ∣ u ∣ p − 2 u + ∣ u ∣ q − 2 u , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. a sufficient and necessary condition is obtained on the existence of nontrivial radial solutions.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46259460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we show continuity of commutators of Calderón-Zygmund operators [ b , T ] left[b,T] with BMO functions in generalized Orlicz-Morrey spaces M Φ , φ ( R n ) {M}^{Phi ,varphi }left({{mathbb{R}}}^{n}) . We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T T and for their commutators [ b , T ] left[b,T] on generalized Orlicz-Morrey spaces, respectively.
{"title":"Characterizations for the genuine Calderón-Zygmund operators and commutators on generalized Orlicz-Morrey spaces","authors":"V. Guliyev, Meriban N. Omarova, M. Ragusa","doi":"10.1515/anona-2022-0307","DOIUrl":"https://doi.org/10.1515/anona-2022-0307","url":null,"abstract":"Abstract In this article, we show continuity of commutators of Calderón-Zygmund operators [ b , T ] left[b,T] with BMO functions in generalized Orlicz-Morrey spaces M Φ , φ ( R n ) {M}^{Phi ,varphi }left({{mathbb{R}}}^{n}) . We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T T and for their commutators [ b , T ] left[b,T] on generalized Orlicz-Morrey spaces, respectively.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44624523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in R 3 {{mathbb{R}}}^{3} , which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the L p {L}^{p} -in-time and L q {L}^{q} -in-space setting with ( p , q ) ∈ ( 2 , ∞ ) × ( 3 , ∞ ) left(p,q)in left(2,infty )times left(3,infty ) satisfying 2 / p + 3 / q < 1 2hspace{0.1em}text{/}p+3text{/}hspace{0.1em}qlt 1 , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.
{"title":"Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension","authors":"Keiichi Watanabe","doi":"10.1515/anona-2022-0279","DOIUrl":"https://doi.org/10.1515/anona-2022-0279","url":null,"abstract":"Abstract This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in R 3 {{mathbb{R}}}^{3} , which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the L p {L}^{p} -in-time and L q {L}^{q} -in-space setting with ( p , q ) ∈ ( 2 , ∞ ) × ( 3 , ∞ ) left(p,q)in left(2,infty )times left(3,infty ) satisfying 2 / p + 3 / q < 1 2hspace{0.1em}text{/}p+3text{/}hspace{0.1em}qlt 1 , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44851901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries. The blood is modeled by the incompressible Navier-Stokes equation, while the motion of vessels is captured by a quasi-stationary equation of nonlinear elasticity. The growth happens when both cells in fluid and solid react, diffuse and transport across the interface, resulting in the accumulation of foam cells, which are exactly seen as the plaques. Via a fixed-point argument, we derive the local well-posedness of the nonlinear system, which is sustained by the analysis of decoupled linear systems.
{"title":"Short-time existence of a quasi-stationary fluid–structure interaction problem for plaque growth","authors":"Helmut Abels, Yadong Liu","doi":"10.1515/anona-2023-0101","DOIUrl":"https://doi.org/10.1515/anona-2023-0101","url":null,"abstract":"Abstract We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries. The blood is modeled by the incompressible Navier-Stokes equation, while the motion of vessels is captured by a quasi-stationary equation of nonlinear elasticity. The growth happens when both cells in fluid and solid react, diffuse and transport across the interface, resulting in the accumulation of foam cells, which are exactly seen as the plaques. Via a fixed-point argument, we derive the local well-posedness of the nonlinear system, which is sustained by the analysis of decoupled linear systems.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we consider the following Choquard system in R N N ≥ 1 {{mathbb{R}}}^{N}Nge 1 − Δ u + u = 2 p p + q ( I α ∗ ∣ v ∣ q ) ∣ u ∣ p − 2 u , − Δ v + v = 2 q p + q ( I α ∗ ∣ u ∣ p ) ∣ v ∣ q − 2 v , u ( x ) → 0 , v ( x ) → 0 as ∣ x ∣ → ∞ , left{begin{array}{l}-Delta u+u=frac{2p}{p+q}({I}_{alpha }ast | v{| }^{q})| u{| }^{p-2}u, -Delta v+v=frac{2q}{p+q}({I}_{alpha }ast | u{| }^{p})| v{| }^{q-2}v, uleft(x)to 0,vleft(x)to 0hspace{1em}hspace{0.1em}text{as}hspace{0.1em}hspace{0.33em}| x| to infty ,end{array}right. where N + α N < p , q < N + α N − 2 frac{N+alpha }{N}lt p,qlt frac{N+alpha }{N-2} , 2 ∗ α {2}_{ast }^{alpha } denotes N + α N − 2 frac{N+alpha }{N-2} if N ≥ 3 Nge 3 and 2 ∗ α ≔ ∞ {2}_{ast }^{alpha }:= infty if N = 1 , 2 N=1,2 , I α {I}_{alpha } is a Riesz potential. By analyzing the asymptotic behavior of Riesz potential energy, we prove that minimal action sign-changing solutions have an odd symmetry with respect to the a hyperplane when α alpha is either close to 0 or close to N N . Our results can be regarded as a generalization of the results by Ruiz et al.
抽象在这个文章,我们认为《R N N≥1跟踪Choquard系统{{R mathbb {}}} ^ {N, N ge 1−Δu + u = 2 p p + q (Iα∗∣v∣q)∣你∣p−2,−Δv + v = 2 q p + q (Iα∗∣u∣p)∣v∣q−2 v, u (x)→0,v (x) x→0美国∣∣→∞,向左拐{开始{}{}- l阵 u + u =三角洲frac {2p} {p + q} ({I}{阿尔法的在的| v {|} q ^ {}) | u u ^ {p - 2},{|的 - Delta v + v = frac {2q} {p + q} ({I}{阿尔法的在的| u {|} p ^ {}) | v ^ {q-2}{|的v,剩下 u (x)到0,v 向左拐(x)到0 hspace {1em} hspace{0。1em} 短信美国{}hspace{0。1em} hspace x{0。33em} | |到 infty, end{阵列的好。哪里N +α< p, q < N +αN−2 frac {N + 阿尔法}{}中尉p, q frac {N + 阿尔法}{已经开始的,2∗的α{2}{在}^{阿尔法的denotes N +αN−2 frac {N + 阿尔法}{已经开始,如果N≥3 ge 3和2∗α≔∞的{2}{在}^{}:=阿尔法 infty如果N = 1, 2的N = 120,我α{}{阿尔法}是一个Riesz申请表。asymptotic社会行为》由analyzing Riesz潜在的能源,我们至少证明那个sign-changing解决方案有一个奇怪的动作和尊重《百万hyperplane symmetry当α阿尔法是要么接近0或接近N N。我们的建议可以作为鲁伊斯和艾尔的代言。
{"title":"Symmetry and nonsymmetry of minimal action sign-changing solutions for the Choquard system","authors":"Jianqing Chen, Qian Zhang","doi":"10.1515/anona-2022-0286","DOIUrl":"https://doi.org/10.1515/anona-2022-0286","url":null,"abstract":"Abstract In this article, we consider the following Choquard system in R N N ≥ 1 {{mathbb{R}}}^{N}Nge 1 − Δ u + u = 2 p p + q ( I α ∗ ∣ v ∣ q ) ∣ u ∣ p − 2 u , − Δ v + v = 2 q p + q ( I α ∗ ∣ u ∣ p ) ∣ v ∣ q − 2 v , u ( x ) → 0 , v ( x ) → 0 as ∣ x ∣ → ∞ , left{begin{array}{l}-Delta u+u=frac{2p}{p+q}({I}_{alpha }ast | v{| }^{q})| u{| }^{p-2}u, -Delta v+v=frac{2q}{p+q}({I}_{alpha }ast | u{| }^{p})| v{| }^{q-2}v, uleft(x)to 0,vleft(x)to 0hspace{1em}hspace{0.1em}text{as}hspace{0.1em}hspace{0.33em}| x| to infty ,end{array}right. where N + α N < p , q < N + α N − 2 frac{N+alpha }{N}lt p,qlt frac{N+alpha }{N-2} , 2 ∗ α {2}_{ast }^{alpha } denotes N + α N − 2 frac{N+alpha }{N-2} if N ≥ 3 Nge 3 and 2 ∗ α ≔ ∞ {2}_{ast }^{alpha }:= infty if N = 1 , 2 N=1,2 , I α {I}_{alpha } is a Riesz potential. By analyzing the asymptotic behavior of Riesz potential energy, we prove that minimal action sign-changing solutions have an odd symmetry with respect to the a hyperplane when α alpha is either close to 0 or close to N N . Our results can be regarded as a generalization of the results by Ruiz et al.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44885067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Soraya Fareh, K. Akrout, A. Ghanmi, Dušan D. Repovš
Abstract In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional p p -Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems.
{"title":"Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities","authors":"Soraya Fareh, K. Akrout, A. Ghanmi, Dušan D. Repovš","doi":"10.1515/anona-2022-0318","DOIUrl":"https://doi.org/10.1515/anona-2022-0318","url":null,"abstract":"Abstract In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional p p -Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42239069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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