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Advances in Differential Equations最新文献

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On a class of $p(x)$-Laplacian equations without any growth and Ambrosetti-Rabinowitz conditions 关于一类不存在任何增长和Ambrosetti-Rabinowitz条件的$p（x）$-Laplacian方程
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-04-01 DOI: 10.57262/ade026-0506-259
Xiaofei Cao, B. Ge, Beilei Zhang
{"title":"On a class of $p(x)$-Laplacian equations without any growth and Ambrosetti-Rabinowitz conditions","authors":"Xiaofei Cao, B. Ge, Beilei Zhang","doi":"10.57262/ade026-0506-259","DOIUrl":"https://doi.org/10.57262/ade026-0506-259","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49285739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Existence of two positive solutions for anisotropic nonlinear elliptic equations 各向异性非线性椭圆型方程两个正解的存在性
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-04-01 DOI: 10.57262/ade026-0506-229
G. Bonanno, G. D'Aguí, A. Sciammetta
{"title":"Existence of two positive solutions for anisotropic nonlinear elliptic equations","authors":"G. Bonanno, G. D'Aguí, A. Sciammetta","doi":"10.57262/ade026-0506-229","DOIUrl":"https://doi.org/10.57262/ade026-0506-229","url":null,"abstract":". This paper deals with the existence of nontrivial solutions for a class of nonlinear elliptic equations driven by an anisotropic Laplacian operator. In particular, the existence of two nontrivial solutions is obtained, adapting a two critical point result to a suitable functional framework that involves the anisotropic Sobolev spaces.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46605541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Existence of weak solutions to the two-dimensional incompressible Euler equations in the presence of sources and sinks 存在源和汇的二维不可压缩Euler方程弱解的存在性
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-03-25 DOI: 10.57262/ade027-1112-683
M. Bravin, F. Sueur
{"title":"Existence of weak solutions to the two-dimensional incompressible Euler equations in the presence of sources and sinks","authors":"M. Bravin, F. Sueur","doi":"10.57262/ade027-1112-683","DOIUrl":"https://doi.org/10.57262/ade027-1112-683","url":null,"abstract":"A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich’s paper [44] in 1966. In this model, on the one hand, the normal component of the fluid velocity is prescribed on the boundary and is nonzero on an open subset of the boundary, corresponding either to sources (where the flow is incoming) or to sinks (where the flow is outgoing). On the other hand the vorticity of the fluid which is entering into the domain from the sources is prescribed. In this paper we investigate the existence of weak solutions to this system by relying on a priori bounds of the vorticity, which satisfies a transport equation associated with the fluid velocity vector field. Our results cover the case where the vorticity has a Lp integrability in space, with p in [1,+∞], and prove the existence of solutions obtained by compactness methods from viscous approximations. More precisely we prove the existence of solutions which satisfy the vorticity equation in the distributional sense in the case where p > 4 3 , in the renormalized sense in the case where p > 1, and in a symmetrized sense in the case where p = 1.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42295545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
An apparently unnatural estimate about forward-backward parabolic equations 这显然是对前后抛物方程的非自然估计
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-03-01 DOI: 10.57262/ade026-0304-133
F. Paronetto
{"title":"An apparently unnatural estimate about forward-backward parabolic equations","authors":"F. Paronetto","doi":"10.57262/ade026-0304-133","DOIUrl":"https://doi.org/10.57262/ade026-0304-133","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49272085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Trajectory statistical solutions and Liouville type theorem for nonlinear wave equations with polynomial growth 多项式增长非线性波动方程的轨迹统计解和Liouville型定理
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-03-01 DOI: 10.57262/ade026-0304-107
Huite Jiang, Caidi Zhao
{"title":"Trajectory statistical solutions and Liouville type theorem for nonlinear wave equations with polynomial growth","authors":"Huite Jiang, Caidi Zhao","doi":"10.57262/ade026-0304-107","DOIUrl":"https://doi.org/10.57262/ade026-0304-107","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42054359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 12
Normalized ground states to a cooperative system of Schrödinger equations with generic $L^2$-subcritical or $L^2$-critical nonlinearity 具有$L^2$-亚临界或$L^2$-临界非线性的Schrödinger方程合作系统的归一化基态
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-01-08 DOI: 10.57262/ade027-0708-467
Jacopo Schino
{"title":"Normalized ground states to a cooperative system of Schrödinger equations with generic $L^2$-subcritical or $L^2$-critical nonlinearity","authors":"Jacopo Schino","doi":"10.57262/ade027-0708-467","DOIUrl":"https://doi.org/10.57262/ade027-0708-467","url":null,"abstract":"We look for ground state solutions to the Schödinger-type system    −∆uj + λjuj = ∂jF (u) ∫ R u2j dx = a 2 j (λj , uj) ∈ R×H1(RN ) j ∈ {1, . . . ,M} with N ≥ 1 and 1 ≤ M < 2 + 4/N , where a = (a1, . . . , aM ) ∈]0,∞[M is prescribed and (λ, u) = (λ1, . . . , λM , u1, . . . uM ) is the unknown. We provide generic assumptions on the nonlinearity F which correspond to the L-subcritical and L-critical cases, i.e., when the energy is bounded from below for all or some values of a. Making use of a recent idea, we minimize the energy over the constraint { |uj |L2 ≤ aj for all j } and then provide further assumptions that ensure |uj |L2 = aj .","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44222008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Multiplicity and concentration results for local and fractional NLS equations with critical growth 具有临界增长的局部和分数阶NLS方程的多重性和集中性结果
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-01-02 DOI: 10.57262/ade026-0910-397
Marco Gallo
{"title":"Multiplicity and concentration results for local and fractional NLS equations with critical growth","authors":"Marco Gallo","doi":"10.57262/ade026-0910-397","DOIUrl":"https://doi.org/10.57262/ade026-0910-397","url":null,"abstract":"Goal of this paper is to study positive semiclassical solutions of the nonlinear Schrodinger equation $$ varepsilon^{2s}(- Delta)^s u+ V(x) u= f(u), quad x in mathbb{R}^N,$$ where $s in (0,1)$, $N geq 2$, $V in C(mathbb{R}^N,mathbb{R})$ is a positive potential and $f$ is assumed critical and satisfying general Berestycki-Lions type conditions. We obtain existence and multiplicity for $varepsilon>0$ small, where the number of solutions is related to the cup-length of a set of local minima of $V$. Furthermore, these solutions are proved to concentrate in the potential well, exhibiting a polynomial decay. We highlight that these results are new also in the limiting local setting $s=1$ and $Ngeq 3$, with an exponential decay of the solutions.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48146472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Strong attractors and their continuity for the semilinear wave equations with fractional damping 分数阶阻尼半线性波动方程的强吸引子及其连续性
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-01-01 DOI: 10.57262/ade/1610420434
Yanan Li, Zhijian Yang
{"title":"Strong attractors and their continuity for the semilinear wave equations with fractional damping","authors":"Yanan Li, Zhijian Yang","doi":"10.57262/ade/1610420434","DOIUrl":"https://doi.org/10.57262/ade/1610420434","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42691774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 6
Existence and $W^{1,p}$ estimates of certain Maxwell type equations in Reifenberg domains Reifenberg域上某些Maxwell型方程的存在性及$W^{1,p}$估计
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2021-01-01 DOI: 10.57262/ade/1610420435
Zhihong Chen, Dongsheng Li
{"title":"Existence and $W^{1,p}$ estimates of certain Maxwell type equations in Reifenberg domains","authors":"Zhihong Chen, Dongsheng Li","doi":"10.57262/ade/1610420435","DOIUrl":"https://doi.org/10.57262/ade/1610420435","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46159920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Global weak solutions to the Navier-Stokes-Darcy-Boussinesq system for thermal convection in coupled free and porous media flows 自由和多孔介质流动中热对流的Navier-Stokes-Darcy-Boussinesq系统的全局弱解
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2020-11-23 DOI: 10.57262/ade/1610420433
Xiaoming Wang, Hao Wu
{"title":"Global weak solutions to the Navier-Stokes-Darcy-Boussinesq system for thermal convection in coupled free and porous media flows","authors":"Xiaoming Wang, Hao Wu","doi":"10.57262/ade/1610420433","DOIUrl":"https://doi.org/10.57262/ade/1610420433","url":null,"abstract":"We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we prove existence of global weak solutions to the initial boundary value problem subject to the Lions and Beavers-Joseph-Saffman-Jones interface conditions. The proof is based on a proper time-implicit discretization scheme combined the compactness argument. Next, we establish a weak-strong uniqueness result such that a weak solution coincides with a strong solution emanating from the same initial data as long as the latter exists.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47483482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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