Pub Date : 2024-06-05DOI: 10.1186/s13661-024-01869-9
Mohamed Azouz, R. Benabidallah, F. Ebobisse
{"title":"On steady state of viscous compressible heat conducting full magnetohydrodynamic equations","authors":"Mohamed Azouz, R. Benabidallah, F. Ebobisse","doi":"10.1186/s13661-024-01869-9","DOIUrl":"https://doi.org/10.1186/s13661-024-01869-9","url":null,"abstract":"","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"11 8","pages":"1-28"},"PeriodicalIF":1.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141265572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.1186/s13661-024-01883-x
Nazarbay Bliev, Nurlan Yerkinbayev
In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuous functions. We indicate a new class of Cauchy-type integrals, which are continuous on a closed domain with continuous (not Hölder) density in terms of Besov spaces, and for which the Sokhotski–Plemelj formulas are valid.
{"title":"Riemann problem for multiply connected domain in Besov spaces","authors":"Nazarbay Bliev, Nurlan Yerkinbayev","doi":"10.1186/s13661-024-01883-x","DOIUrl":"https://doi.org/10.1186/s13661-024-01883-x","url":null,"abstract":"In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuous functions. We indicate a new class of Cauchy-type integrals, which are continuous on a closed domain with continuous (not Hölder) density in terms of Besov spaces, and for which the Sokhotski–Plemelj formulas are valid.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"36 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.1186/s13661-024-01878-8
Saleh Fahad Aljurbua
This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order $3
本文的重点是利用定点定理探索一类特殊的 FDE 的解的存在性。该方程具有阶数为 $3
{"title":"Exploring solutions to specific class of fractional differential equations of order (3<hat{u}leq 4)","authors":"Saleh Fahad Aljurbua","doi":"10.1186/s13661-024-01878-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01878-8","url":null,"abstract":"This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order $3<hat{u} leq 4$ and includes a term $Theta (beta,mathscr{Z}(beta ))$ alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"26 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-31DOI: 10.1186/s13661-024-01881-z
Jing Zhang
In this paper we study the following nonlinear Schrödinger system: $$ textstylebegin{cases} -Delta u+alpha u = vert u vert ^{p-1}u+frac{2}{q+1} lambda vert u vert ^{ frac{p-3}{2}}u vert v vert ^{frac{q+1}{2}},quad x in mathbb{R}^{3}, -Delta v+beta v = vert v vert ^{q-1}v+frac{2}{p+1} lambda vert u vert ^{ frac{p+1}{2}} vert v vert ^{frac{q-3}{2}}v ,quad x in mathbb{R}^{3}, u(x)rightarrow 0,qquad v(x)rightarrow 0,quad text{as } vert x vert rightarrow infty , end{cases} $$ where $3leq p, q<5$ , α, β are positive parameters. We show that there exists $lambda _{k}>0$ such that the equation has at least k radially symmetric sign-changing solutions and at least k seminodal solutions for each $kin mathbb{N}$ and $lambda in (0, lambda _{k})$ . Moreover, we show the existence of a least energy radially symmetric sign-changing solution for each $lambda in (0, lambda _{0})$ where $lambda _{0}in (0, lambda _{1}]$ .
本文将研究以下非线性薛定谔系统： $$ （textstylebegin{cases} -Delta u+alpha u = vert u vert ^{p-1}u+frac{2}{q+1}lambda vert u vert ^{frac{p-3}{2}}u vert v vert ^{frac{q+1}{2}}, quad x in mathbb{R}^{3}, -Delta v+beta v = vert v vert ^{q-1}v+frac{2}{p+1}vert u vert ^{ frac{p+1}{2}vert v vert ^{frac{q-3}{2}v ,quad x in mathbb{R}^{3}, u(x)rightarrow 0,qquad v(x)rightarrow 0,quad text{as }vert x vert rightarrow infty , end{cases} $$ 其中 $3leq p, q0$ 使得方程在每个 $kin mathbb{N}$ 和 $lambda in (0, lambda _{k})$ 中至少有 k 个径向对称的符号变化解和至少 k 个半径解。此外，我们证明了每个 $lambda in (0, lambda _{0})$（其中 $lambda _{0}in（0, lambda _{1}]$）都存在能量最小的径向对称符号变化解。
{"title":"Sign-changing solutions for coupled Schrödinger system","authors":"Jing Zhang","doi":"10.1186/s13661-024-01881-z","DOIUrl":"https://doi.org/10.1186/s13661-024-01881-z","url":null,"abstract":"In this paper we study the following nonlinear Schrödinger system: $$ textstylebegin{cases} -Delta u+alpha u = vert u vert ^{p-1}u+frac{2}{q+1} lambda vert u vert ^{ frac{p-3}{2}}u vert v vert ^{frac{q+1}{2}},quad x in mathbb{R}^{3}, -Delta v+beta v = vert v vert ^{q-1}v+frac{2}{p+1} lambda vert u vert ^{ frac{p+1}{2}} vert v vert ^{frac{q-3}{2}}v ,quad x in mathbb{R}^{3}, u(x)rightarrow 0,qquad v(x)rightarrow 0,quad text{as } vert x vert rightarrow infty , end{cases} $$ where $3leq p, q<5$ , α, β are positive parameters. We show that there exists $lambda _{k}>0$ such that the equation has at least k radially symmetric sign-changing solutions and at least k seminodal solutions for each $kin mathbb{N}$ and $lambda in (0, lambda _{k})$ . Moreover, we show the existence of a least energy radially symmetric sign-changing solution for each $lambda in (0, lambda _{0})$ where $lambda _{0}in (0, lambda _{1}]$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-29DOI: 10.1186/s13661-024-01877-9
Tahar Bouali, Rafik Guefaifia, Salah Boulaaras
In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents. Our approach is mainly based on the sub-supersolution method and the mountain pass theorem.
{"title":"Fractional double-phase nonlocal equation in Musielak-Orlicz Sobolev space","authors":"Tahar Bouali, Rafik Guefaifia, Salah Boulaaras","doi":"10.1186/s13661-024-01877-9","DOIUrl":"https://doi.org/10.1186/s13661-024-01877-9","url":null,"abstract":"In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents. Our approach is mainly based on the sub-supersolution method and the mountain pass theorem.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"7 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-27DOI: 10.1186/s13661-024-01873-z
A. A. El-Gaber
The oscillatory behavior of solutions of an even-order differential equation with a superlinear neutral term is considered using Riccati and generalized Riccati transformations, the integral averaging technique, and the theory of comparison. New sufficient conditions are established in the noncanonical case. An example is given to support our results.
{"title":"Oscillatory criteria of noncanonical even-order differential equations with a superlinear neutral term","authors":"A. A. El-Gaber","doi":"10.1186/s13661-024-01873-z","DOIUrl":"https://doi.org/10.1186/s13661-024-01873-z","url":null,"abstract":"The oscillatory behavior of solutions of an even-order differential equation with a superlinear neutral term is considered using Riccati and generalized Riccati transformations, the integral averaging technique, and the theory of comparison. New sufficient conditions are established in the noncanonical case. An example is given to support our results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"7 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141173417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-20DOI: 10.1186/s13661-024-01871-1
Tetsutaro Shibata
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_{lambda}$ and bifurcation curves $lambda (alpha )$ , where $alpha := Vert u_{lambda}Vert _{infty}$ .
{"title":"Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions","authors":"Tetsutaro Shibata","doi":"10.1186/s13661-024-01871-1","DOIUrl":"https://doi.org/10.1186/s13661-024-01871-1","url":null,"abstract":"We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_{lambda}$ and bifurcation curves $lambda (alpha )$ , where $alpha := Vert u_{lambda}Vert _{infty}$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"28 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-17DOI: 10.1186/s13661-024-01872-0
Gohar Ali, Rahman Ullah Khan, Kamran, Ahmad Aloqaily, Nabil Mlaiki
A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings.
{"title":"On qualitative analysis of a fractional hybrid Langevin differential equation with novel boundary conditions","authors":"Gohar Ali, Rahman Ullah Khan, Kamran, Ahmad Aloqaily, Nabil Mlaiki","doi":"10.1186/s13661-024-01872-0","DOIUrl":"https://doi.org/10.1186/s13661-024-01872-0","url":null,"abstract":"A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"50 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1186/s13661-024-01862-2
A. S. Dawood, Faisal A. Kroush, Ramzy M. Abumandour, Islam M. Eldesoky
A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.
{"title":"Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study","authors":"A. S. Dawood, Faisal A. Kroush, Ramzy M. Abumandour, Islam M. Eldesoky","doi":"10.1186/s13661-024-01862-2","DOIUrl":"https://doi.org/10.1186/s13661-024-01862-2","url":null,"abstract":"A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"161 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-13DOI: 10.1186/s13661-024-01868-w
Hai-yun Deng, Xiao-yan Lin, Yu-bo He
In this paper, we consider a $(phi _{1},phi _{2})$ -Laplacian system as follows: $$begin{aligned} textstylebegin{cases} Delta phi _{1} (Delta u(t-1) )+nabla _{u} F(t,u(t),v(t))=0, Delta phi _{2} (Delta v(t-1) )+nabla _{v} F(t,u(t),v(t))=0, end{cases}displaystyle end{aligned}$$ where $F(t,u(t),v(t))=-K(t,u(t),v(t))+W(t,u(t),v(t))$ is T-periodic in t. By using the mountain pass theorem, we obtain that the $(phi _{1},phi _{2})$ -Laplacian system has at least one periodic solution if W is asymptotically $(p,q)$ -linear at infinity. Our results improve and extend some known works.
{"title":"Existence of periodic solutions for a class of ((phi _{1},phi _{2}))-Laplacian difference system with asymptotically ((p,q))-linear conditions","authors":"Hai-yun Deng, Xiao-yan Lin, Yu-bo He","doi":"10.1186/s13661-024-01868-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01868-w","url":null,"abstract":"In this paper, we consider a $(phi _{1},phi _{2})$ -Laplacian system as follows: $$begin{aligned} textstylebegin{cases} Delta phi _{1} (Delta u(t-1) )+nabla _{u} F(t,u(t),v(t))=0, Delta phi _{2} (Delta v(t-1) )+nabla _{v} F(t,u(t),v(t))=0, end{cases}displaystyle end{aligned}$$ where $F(t,u(t),v(t))=-K(t,u(t),v(t))+W(t,u(t),v(t))$ is T-periodic in t. By using the mountain pass theorem, we obtain that the $(phi _{1},phi _{2})$ -Laplacian system has at least one periodic solution if W is asymptotically $(p,q)$ -linear at infinity. Our results improve and extend some known works.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"18 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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