In this work first we transform the semi-noncanonical fourth order neutral delay differential equations into canonical type. This simplifies the investigations of finding the relationships between the solution and its companion function which plays an important role in the oscillation theory of neutral differential equations. Moreover, we improve these relationships based on the monotonic properties of positive solutions. We present new conditions for the oscillation of all solutions of the corresponding equation which improve the oscillation results already reported in the literature. Examples are provided to illustrate the importance of our main results. For moreinformation see https://ejde.math.txstate.edu/Volumes/2023/70/abstr.html
{"title":"Oscillation criteria of fourth-order nonlinear semi-noncanonical neutral differential equations via a canonical transform","authors":"Ganesh Purushothaman, Kannan Suresh, Ercan Tunc, Ethiraju Thandapani","doi":"10.58997/ejde.2023.70","DOIUrl":"https://doi.org/10.58997/ejde.2023.70","url":null,"abstract":"In this work first we transform the semi-noncanonical fourth order neutral delay differential equations into canonical type. This simplifies the investigations of finding the relationships between the solution and its companion function which plays an important role in the oscillation theory of neutral differential equations. Moreover, we improve these relationships based on the monotonic properties of positive solutions. We present new conditions for the oscillation of all solutions of the corresponding equation which improve the oscillation results already reported in the literature. Examples are provided to illustrate the importance of our main results. For moreinformation see https://ejde.math.txstate.edu/Volumes/2023/70/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136142332","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}
In this article, we consider the Kirchhoff plate equation with delay terms on the boundary control. We give instability examples of systems for some choices of delays. Finally, we prove its well-posedness, strong stability, and exponential stability under a multiplier geometric control condition.
Foro more information see https://ejde.math.txstate.edu/Volumes/2023/68/abstr.html
{"title":"Stability and instability of Kirchhoff plate equations with delay on the boundary control","authors":"Haidar Badawi, Mohammad Akil, Zayd Hajjej","doi":"10.58997/ejde.2023.68","DOIUrl":"https://doi.org/10.58997/ejde.2023.68","url":null,"abstract":"In this article, we consider the Kirchhoff plate equation with delay terms on the boundary control. We give instability examples of systems for some choices of delays. Finally, we prove its well-posedness, strong stability, and exponential stability under a multiplier geometric control condition.
 Foro more information see https://ejde.math.txstate.edu/Volumes/2023/68/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"223 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136142208","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}
In this article, we prove boundedness for the Hessian of a Schrodinger operator with weak regularity on the coefficients, and potentials satisfying the reverse H"older condition. This is done in in generalized Morrey spaces, and in vanishing generalized Morrey spaces. On the Schrodinger operator (L=-a_{ij}(x)D_{ij}+V(x)) it is assumed that (a_{ij}in rm{BMO}_{theta}(rho)) (a generalized Morrey space) and that (V(x)in B^*_{n/2}) (a reverse Holder class).
For more information see https://ejde.math.txstate.edu/Volumes/2023/67/abstr.html
{"title":"Boundedness on generalized Morrey spaces for the Schrodinger operator with potential in a reverse Holder class","authors":"Guiyun Wang, Shenzhou Zheng","doi":"10.58997/ejde.2023.67","DOIUrl":"https://doi.org/10.58997/ejde.2023.67","url":null,"abstract":"In this article, we prove boundedness for the Hessian of a Schrodinger operator with weak regularity on the coefficients, and potentials satisfying the reverse H\"older condition. This is done in in generalized Morrey spaces, and in vanishing generalized Morrey spaces. On the Schrodinger operator (L=-a_{ij}(x)D_{ij}+V(x)) it is assumed that (a_{ij}in rm{BMO}_{theta}(rho)) (a generalized Morrey space) and that (V(x)in B^*_{n/2}) (a reverse Holder class).
 For more information see https://ejde.math.txstate.edu/Volumes/2023/67/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918286","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}
We study the existence and multiplicity of solutions for the Schrodinger-Bopp-Podolsky system $$displaylines{ -Delta u + phi u = omega u quadtext{ in } Omega cr a^2Delta^2phi-Delta phi = u^2 quadtext{ in } Omega cr u=phi=Deltaphi=0quadtext{ on } partialOmega cr int_{Omega} u^2,dx =1 }$$ where (Omega) is an open bounded and smooth domain in (mathbb R^{3}), (a>0 ) is the Bopp-Podolsky parameter. The unknowns are (u,phi:Omegato mathbb R) and (omegainmathbb R). By using variational methods we show that for any (a>0) there are infinitely many solutions with diverging energy and divergent in norm. We show that ground states solutions converge to a ground state solution of the related classical Schrodinger-Poisson system, as (ato 0). For more information see https://ejde.math.txstate.edu/Volumes/2023/66/abstr.html
我们研究了Schrodinger-Bopp-Podolsky系统$$displaylines{ -Delta u + phi u = omega u quadtext{ in } Omega cr a^2Delta^2phi-Delta phi = u^2 quadtext{ in } Omega cr u=phi=Deltaphi=0quadtext{ on } partialOmega cr int_{Omega} u^2,dx =1 }$$的解的存在性和多重性，其中(Omega)为(mathbb R^{3})中的开有界光滑域，(a>0 )为Bopp-Podolsky参数。未知数是(u,phi:Omegato mathbb R)和(omegainmathbb R)。利用变分方法证明了对于任意(a>0)存在无穷多个能量发散且范数发散的解。我们证明了基态解收敛于相关的经典薛定谔-泊松系统的基态解，如(ato 0)。欲了解更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/66/abstr.html
{"title":"Existence and asymptotic behavior of solutions to eigenvalue problems for Schrodinger-Bopp-Podolsky equations","authors":"Lorena Soriano Hernandez, Gaetano Siciliano","doi":"10.58997/ejde.2023.66","DOIUrl":"https://doi.org/10.58997/ejde.2023.66","url":null,"abstract":"We study the existence and multiplicity of solutions for the Schrodinger-Bopp-Podolsky system $$displaylines{ -Delta u + phi u = omega u quadtext{ in } Omega cr a^2Delta^2phi-Delta phi = u^2 quadtext{ in } Omega cr u=phi=Deltaphi=0quadtext{ on } partialOmega cr int_{Omega} u^2,dx =1 }$$ where (Omega) is an open bounded and smooth domain in (mathbb R^{3}), (a>0 ) is the Bopp-Podolsky parameter. The unknowns are (u,phi:Omegato mathbb R) and (omegainmathbb R). By using variational methods we show that for any (a>0) there are infinitely many solutions with diverging energy and divergent in norm. We show that ground states solutions converge to a ground state solution of the related classical Schrodinger-Poisson system, as (ato 0). For more information see https://ejde.math.txstate.edu/Volumes/2023/66/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918943","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}
We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{lambda}operatorname{sgn} u+mu f(t);quad u(0)=u(omega),; u'(0)=u'(omega), $$ where (muin mathbb{R}) is a parameter. We assume that (p,h,fin L([0,omega])), (lambda>1), and the function (h) is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term (f) to change its sign.
For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html
{"title":"Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term","authors":"Jiri Sremr","doi":"10.58997/ejde.2023.65","DOIUrl":"https://doi.org/10.58997/ejde.2023.65","url":null,"abstract":"We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{lambda}operatorname{sgn} u+mu f(t);quad u(0)=u(omega),; u'(0)=u'(omega), $$ where (muin mathbb{R}) is a parameter. We assume that (p,h,fin L([0,omega])), (lambda>1), and the function (h) is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term (f) to change its sign.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"301 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135546506","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}
In this article, we consider planar Schrodinger-Poisson systems with a logarithmic external potential (W(x)=ln (1+|x|^2)) and a general nonlinear term (f). We obtain conditions for the local well-posedness of the Cauchy problem in the energy space. By introducing some suitable assumptions on (f), we prove the existence of the global minimizer. In addition, with the help of the local well-posedness, we show that the set of ground state standing waves is orbitally stable.
For more information see https://ejde.math.txstate.edu/Volumes/2023/64/abstr.html
{"title":"Local well-posedness and standing waves with prescribed mass for Schrodinger-Poisson systems with a logarithmic potential in R^2","authors":"Xuechao Dou, Juntao Sun","doi":"10.58997/ejde.2023.64","DOIUrl":"https://doi.org/10.58997/ejde.2023.64","url":null,"abstract":"In this article, we consider planar Schrodinger-Poisson systems with a logarithmic external potential (W(x)=ln (1+|x|^2)) and a general nonlinear term (f). We obtain conditions for the local well-posedness of the Cauchy problem in the energy space. By introducing some suitable assumptions on (f), we prove the existence of the global minimizer. In addition, with the help of the local well-posedness, we show that the set of ground state standing waves is orbitally stable.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/64/abstr.html
","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135864035","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}
In this paper, we analyze the abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces by using multivalued linear operators and vector-valued Laplace transform. We follow the method which is based on the use of (a, k)-regularized C-resolvent families generated by multivalued linear operators and which suggests a very general way of approaching abstract Volterra equations. Among many other themes, we consider the Hille-Yosida type theorems for ((a, k))-regularized C-resolvent families, differential and analytical properties of ((a, k))-regularized $C$-resolvent families, the generalized variation of parameters formula, and subordination principles. We also introduce and analyze the class of ((a, k))-regularized ((C_1,C_2))-existence and uniqueness families. The main purpose of third section, which can be viewed of some independent interest, is to introduce a relatively simple and new theoretical concept useful in the analysis of operational properties of Laplace transform of non-continuous functions with values in sequentially complete locally convex spaces. This concept coincides with the classical concept of vector-valued Laplace transform in the case that (X) is a Banach space. For more information see https://ejde.math.txstate.edu/Volumes/2023/63/abstr.html
{"title":"Abstract degenerate Volterra inclusions in locally convex spaces","authors":"Marko Kostic","doi":"10.58997/ejde.2023.63","DOIUrl":"https://doi.org/10.58997/ejde.2023.63","url":null,"abstract":"In this paper, we analyze the abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces by using multivalued linear operators and vector-valued Laplace transform. We follow the method which is based on the use of (a, k)-regularized C-resolvent families generated by multivalued linear operators and which suggests a very general way of approaching abstract Volterra equations. Among many other themes, we consider the Hille-Yosida type theorems for ((a, k))-regularized C-resolvent families, differential and analytical properties of ((a, k))-regularized $C$-resolvent families, the generalized variation of parameters formula, and subordination principles. We also introduce and analyze the class of ((a, k))-regularized ((C_1,C_2))-existence and uniqueness families. The main purpose of third section, which can be viewed of some independent interest, is to introduce a relatively simple and new theoretical concept useful in the analysis of operational properties of Laplace transform of non-continuous functions with values in sequentially complete locally convex spaces. This concept coincides with the classical concept of vector-valued Laplace transform in the case that (X) is a Banach space. For more information see https://ejde.math.txstate.edu/Volumes/2023/63/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135864169","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}
In this article, we study the equatorial shallow-water equations with slip boundary condition in bounded domain. By exploring the dissipative structures of the system, we obtaining a priori estimates of the solution for small initial data. Then the existence of classical global solutions and exponential stability results are given.
For more inofrmation see https://ejde.math.txstate.edu/Volumes/2023/62/abstr.html
{"title":"Global classical solutions to equatorial shallow-water equations","authors":"Yue Fang, Kaiqiang Li, Xin Xu","doi":"10.58997/ejde.2023.62","DOIUrl":"https://doi.org/10.58997/ejde.2023.62","url":null,"abstract":"In this article, we study the equatorial shallow-water equations with slip boundary condition in bounded domain. By exploring the dissipative structures of the system, we obtaining a priori estimates of the solution for small initial data. Then the existence of classical global solutions and exponential stability results are given.
 For more inofrmation see https://ejde.math.txstate.edu/Volumes/2023/62/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136237387","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}
This paper is concerned with existence results for the singular $p$-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. More precisely, by using variational methods combined with the Mountain pass theorem and the Ekeland variational principle, we establish the existence and multiplicity of solutions. To illustrate the usefulness of our results, an illustrative example is also presented.
{"title":"Singular p-biharmonic problems involving the Hardy-Sobolev exponent","authors":"Amor Drissi, Abdeljabbar Ghanmi, Dusan D. Repovs","doi":"10.58997/ejde.2023.61","DOIUrl":"https://doi.org/10.58997/ejde.2023.61","url":null,"abstract":"This paper is concerned with existence results for the singular $p$-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. More precisely, by using variational methods combined with the Mountain pass theorem and the Ekeland variational principle, we establish the existence and multiplicity of solutions. To illustrate the usefulness of our results, an illustrative example is also presented.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135109759","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}
We consider space-time behaviors of smooth solutions for the radiative hydrodynamics system with or without heat conduction in the whole space (R^3) by using Green's function method. This result exhibits the generalized Huygens' principle as the classical compressible Navier-Stokes equations [3,26], which is different from the Hamer model for radiating gases in [36].
For more information see https://ejde.math.txstate.edu/Volumes/2023/60/abstr.html
{"title":"Space-time behavior for radiative hydrodynamics model with or without heat conduction","authors":"Mengqian Liu, Zhigang Wu","doi":"10.58997/ejde.2023.60","DOIUrl":"https://doi.org/10.58997/ejde.2023.60","url":null,"abstract":"We consider space-time behaviors of smooth solutions for the radiative hydrodynamics system with or without heat conduction in the whole space (R^3) by using Green's function method. This result exhibits the generalized Huygens' principle as the classical compressible Navier-Stokes equations [3,26], which is different from the Hamer model for radiating gases in [36].
 For more information see https://ejde.math.txstate.edu/Volumes/2023/60/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"206 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437409","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：