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Electronic Journal of Differential Equations最新文献

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Optimal energy decay rates for viscoelastic wave equations with nonlinearity of variable exponent 变指数非线性粘弹性波动方程的最优能量衰减率
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-08-28 DOI: 10.58997/ejde.2023.53
M. I. Mustafa
{"title":"Optimal energy decay rates for viscoelastic wave equations with nonlinearity of variable exponent","authors":"M. I. Mustafa","doi":"10.58997/ejde.2023.53","DOIUrl":"https://doi.org/10.58997/ejde.2023.53","url":null,"abstract":"In this article, we consider the viscoelastic wave equation $$ u_{tt}-Delta u+int_0^{t}g(t-s)Delta u(s)ds+a| u_t| ^{m(cdot )-2}u_t=0 $$ with a nonlinear feedback having a variable exponent (m(x)). We investigate the interaction between the two types of damping and establish an optimal decay result under very general assumptions on the relaxation function (g). We construct explicit formulae which provide faster energy decay rates than the ones already existing in the literature. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/53/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45970323","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}
引用次数: 0
Existence and nonexistence of positive solutions for fourth-order elliptic problems 四阶椭圆型问题正解的存在性与不存在性
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-08-06 DOI: 10.58997/ejde.2023.52
Meiqiang Feng, Haiping Chen
{"title":"Existence and nonexistence of positive solutions for fourth-order elliptic problems","authors":"Meiqiang Feng, Haiping Chen","doi":"10.58997/ejde.2023.52","DOIUrl":"https://doi.org/10.58997/ejde.2023.52","url":null,"abstract":"This article studies a fourth-order elliptic problem with and without an eigenvalue parameter. New criteria for the existence and nonexistence of positive solution are established under some sublinear conditions which involve the principal eigenvalues of the corresponding linear problems. The interesting point is that the nonlinear term (f) is involved in the second-order derivative explicitly. For more information see https://ejde.math.txstate.edu/Volumes/2023/52/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136043996","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}
引用次数: 0
Existence and uniqueness results for fourth-order four-point BVP arising in bridge design in the presence of reverse ordered upper and lower solutions 桥梁设计中存在逆序上下解的四阶四点BVP问题的存在唯一性结果
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-08-04 DOI: 10.58997/ejde.2023.51
Nazia Urus, Amit Verma
{"title":"Existence and uniqueness results for fourth-order four-point BVP arising in bridge design in the presence of reverse ordered upper and lower solutions","authors":"Nazia Urus, Amit Verma","doi":"10.58997/ejde.2023.51","DOIUrl":"https://doi.org/10.58997/ejde.2023.51","url":null,"abstract":"In this article, we establish the existence of solutions for a fourth-order four-point non-linear boundary value problem (BVP) which arises in bridge design, $$displaylines{ - y^{(4)}( s)-lambda y''( s)=mathcal{F}( s, y( s)), quad sin(0,1),cry(0)=0,quad y(1)= delta_1 y(eta_1)+delta_2 y(eta_2),cr y''(0)=0,quad y''(1)= delta_1 y''(eta_1)+delta_2 y''(eta_2), }$$ where (mathcal{F} in C([0,1]times mathbb{R},mathbb{R})), (delta_1, delta_2>0), (0<eta_1le eta_2 <1), (lambda=zeta_1+zeta_2 ), where (zeta_1) and (zeta_2) are the real constants. We have explored all gathered (0<zeta_1<zeta_2), (zeta_1<0<zeta_2), and ( zeta_1<zeta_2<0 ). We extend the monotone iterative technique and establish the existence results with reverse ordered upper and lower solutions to fourth-orderfour-point non-linear BVPs. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/51/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46165150","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}
引用次数: 0
Evolution equations on time-dependent Lebesgue spaces with variable exponents 变指数时变Lebesgue空间上的演化方程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-07-24 DOI: 10.58997/ejde.2023.50
J. Simsen
{"title":"Evolution equations on time-dependent Lebesgue spaces with variable exponents","authors":"J. Simsen","doi":"10.58997/ejde.2023.50","DOIUrl":"https://doi.org/10.58997/ejde.2023.50","url":null,"abstract":"We extend the results in Kloeden-Simsen [CPAA 2014] to (p(x,t))-Laplacian problems on time-dependent Lebesgue spaces withvariable exponents. We study the equation $$displaylines{  frac{partial u_lambda}{partial t}(t)-operatorname{div}big(D_lambda(t,x)|nabla u_lambda(t)|^{p(x,t)-2}nabla  _lambda(t)big)+|u_lambda(t)|^{p(x,t)-2}u_lambda(t)  =B(t,u_lambda(t)) }$$on a bounded smooth domain (Omega) in (mathbb{R}^n),(ngeq 1), with a homogeneous Neumann boundary condition, where the exponent (p(cdot)in C(bar{Omega}times [tau,T],mathbb{R}^+)) satisfies (min p(x,t)>2), and (lambdain [0,infty)) is a parameter.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/50/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42410358","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}
引用次数: 0
Multiplicity of solutions for a generalized Kadomtsev-Petviashvili equation with potential in R^2 具有R^2位的广义Kadomtsev-Petviashvili方程解的多重性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-07-17 DOI: 10.58997/ejde.2023.48
Zheng Xie, Jing Chen
{"title":"Multiplicity of solutions for a generalized Kadomtsev-Petviashvili equation with potential in R^2","authors":"Zheng Xie, Jing Chen","doi":"10.58997/ejde.2023.48","DOIUrl":"https://doi.org/10.58997/ejde.2023.48","url":null,"abstract":"In this article, we study the generalized Kadomtsev-Petviashvili equation witha potential $$ (-u_{xx}+D_{x}^{-2}u_{yy}+V(varepsilon x,varepsilon y)u-f(u))_{x}=0quad text{in }mathbb{R}^2, $$ where (D_{x}^{-2}h(x,y)=int_{-infty }^{x}int_{-infty }^{t}h(s,y),ds,dt ), (f) is a nonlinearity, (varepsilon) is a small positive parameter, and the potential (V) satisfies a local condition. We prove the existence of nontrivial solitary waves for the modified problem by applying penalization techniques. The relationship between the number of positive solutions and the topology of the set where (V) attains its minimum is obtained by using Ljusternik-Schnirelmann theory. With the help of Moser's iteration method, we verify that the solutions of the modified problem are indeed solutions of the original  roblem for (varepsilon>0) small enough.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45875334","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}
引用次数: 0
Stochastic Burgers equations with fractional derivative driven by fractional noise 分数噪声驱动的分数阶导数随机Burgers方程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-07-17 DOI: 10.58997/ejde.2023.49
Yubo Duan, Yiming Jiang, Yang Tian, Yawei Wei
{"title":"Stochastic Burgers equations with fractional derivative driven by fractional noise","authors":"Yubo Duan, Yiming Jiang, Yang Tian, Yawei Wei","doi":"10.58997/ejde.2023.49","DOIUrl":"https://doi.org/10.58997/ejde.2023.49","url":null,"abstract":"by fractional noise. Existence and uniqueness of a mild solution is given bya fixed point argument. Then, we explore Holder regularity of the mildsolution in (C([0,T_{*}];L^p(Omega;dot{H}^{gamma}))) for some stoppingtime (T_{*}).","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47524717","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}
引用次数: 0
Existence of at least four solutions for Schrodinger equations with magnetic potential involving and sign-changing weight function 含磁势和变号权函数的薛定谔方程至少四个解的存在性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-07-11 DOI: 10.58997/ejde.2023.47
Francisco Odair de Paiva, Sandra Machado de Souza Lima, O. Miyagaki
{"title":"Existence of at least four solutions for Schrodinger equations with magnetic potential involving and sign-changing weight function","authors":"Francisco Odair de Paiva, Sandra Machado de Souza Lima, O. Miyagaki","doi":"10.58997/ejde.2023.47","DOIUrl":"https://doi.org/10.58997/ejde.2023.47","url":null,"abstract":"We consider the elliptic problem $$ - Delta_A u + u = a_{lambda}(x) |u|^{q-2}u+b_{mu}(x) |u|^{p-2}u , $$ for (x in mathbb{R}^N), ( 1 < q < 2 < p < 2^*= 2N/(N-2)), (a_{lambda}(x)) is a sign-changing weight function, (b_{mu}(x)) satisfies some additional conditions, (u in H^1_A(mathbb{R}^N)) and (A:mathbb{R}^N to mathbb{R}^N) is a magnetic potential. Exploring the Bahri-Li argument and some preliminary results we will discuss the existence of a four nontrivial solutions to the problem in question.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46765733","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}
引用次数: 0
Asymptotic behavior of blowup solutions for Henon type parabolic equations with exponential nonlinearity 具有指数非线性的Henon型抛物型方程爆破解的渐近性质
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-07-09 DOI: 10.58997/ejde.2022.42
Caihong Chang, Zhengce Zhang
{"title":"Asymptotic behavior of blowup solutions for Henon type parabolic equations with exponential nonlinearity","authors":"Caihong Chang, Zhengce Zhang","doi":"10.58997/ejde.2022.42","DOIUrl":"https://doi.org/10.58997/ejde.2022.42","url":null,"abstract":"This article concerns the blow up behavior for the Henon type parabolic equation withexponential nonlinearity, $$ u_t=Delta u+|x|^{sigma}e^uquad text{in } B_Rtimes mathbb{R}_+, $$ where (sigmageq 0) and (B_R={xinmathbb{R}^N: |x|<R}).We consider all cases in which blowup of solutions occurs, i.e. (Ngeq 10+4sigma).Grow up rates are established by a certain matching of different asymptotic behaviorsin the inner region (near the singularity) and the outer region (close to the boundary).For the cases (N>10+4sigma) and (N=10+4sigma), the asymptotic expansions of stationary solutions have different forms, so two cases are discussed separately. Moreover, different inner region widths in two cases are also obtained.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48470912","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}
引用次数: 0
Existence and multiplicity of solutions to a fractional p-Laplacian elliptic Dirichlet problem 一个分数阶p-Laplace椭圆Dirichlet问题解的存在性和多重性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-07-03 DOI: 10.58997/ejde.2023.46
Fariba Gharehgazlouei, J. Graef, S. Heidarkhani, L. Kong
{"title":"Existence and multiplicity of solutions to a fractional p-Laplacian elliptic Dirichlet problem","authors":"Fariba Gharehgazlouei, J. Graef, S. Heidarkhani, L. Kong","doi":"10.58997/ejde.2023.46","DOIUrl":"https://doi.org/10.58997/ejde.2023.46","url":null,"abstract":"In this article, the authors consider a fractional p-Laplacian elliptic Dirichlet problem. Using critical point theory and the variational method, they investigate the existence of at least one, two, and three solutions to the problem. Examples illustrating the results are interspaced in the paper.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47168386","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}
引用次数: 1
Oscillation criteria for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term 具有超线性中立项的非正则二阶非线性时滞差分方程的振动判据
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-29 DOI: 10.58997/ejde.2023.45
K. Vidhyaa, E. Thandapani, J. Alzabut, Abdullah Ozbekler
{"title":"Oscillation criteria for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term","authors":"K. Vidhyaa, E. Thandapani, J. Alzabut, Abdullah Ozbekler","doi":"10.58997/ejde.2023.45","DOIUrl":"https://doi.org/10.58997/ejde.2023.45","url":null,"abstract":"We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to (0) or (infty). Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examplesthat cannot be included in earlier works.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45381927","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}
引用次数: 0
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