Pub Date : 2021-09-01DOI: 10.57262/ade026-0910-425
Siyu Chen, C. Santos, Minbo Yang, Jiazheng Zhou
{"title":"Global multiplicity of solutions for a quasilinear elliptic equation with concave and convex nonlinearities","authors":"Siyu Chen, C. Santos, Minbo Yang, Jiazheng Zhou","doi":"10.57262/ade026-0910-425","DOIUrl":"https://doi.org/10.57262/ade026-0910-425","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41825166","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}
Pub Date : 2021-09-01DOI: 10.57262/ade026-0910-505
D. Arcoya, L. Boccardo, L. Orsina
{"title":"Schrödinger-Maxwell systems with interplay between coefficients and data","authors":"D. Arcoya, L. Boccardo, L. Orsina","doi":"10.57262/ade026-0910-505","DOIUrl":"https://doi.org/10.57262/ade026-0910-505","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43464652","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}
Pub Date : 2021-07-28DOI: 10.57262/ade027-1112-823
Andrew Colinet
In the setting of a compact Riemannian manifold of dimension N ≥ 3 we provide a structural description of the limiting behaviour of the energy measures of solutions to the parabolic Ginzburg-Landau equation. In particular, we provide a decomposition of the limiting energy measure into a diffuse part, which is absolutely continuous with respect to the volume measure, and a concentrated part supported on a codimension 2 rectifiable subset. We also demonstrate that the time evolution of the diffuse part is determined by the heat equation while the concentrated part evolves according to a Brakke flow. This paper extends the work of Bethuel, Orlandi, and Smets from [8].
{"title":"Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds","authors":"Andrew Colinet","doi":"10.57262/ade027-1112-823","DOIUrl":"https://doi.org/10.57262/ade027-1112-823","url":null,"abstract":"In the setting of a compact Riemannian manifold of dimension N ≥ 3 we provide a structural description of the limiting behaviour of the energy measures of solutions to the parabolic Ginzburg-Landau equation. In particular, we provide a decomposition of the limiting energy measure into a diffuse part, which is absolutely continuous with respect to the volume measure, and a concentrated part supported on a codimension 2 rectifiable subset. We also demonstrate that the time evolution of the diffuse part is determined by the heat equation while the concentrated part evolves according to a Brakke flow. This paper extends the work of Bethuel, Orlandi, and Smets from [8].","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47474334","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}
Pub Date : 2021-06-30DOI: 10.57262/ade028-0304-287
Camilla Brizzi, L. Pascale
We discover a new minimality property of the absolute minimizers of supremal functionals, whose variational problems are also known as L ∞ variational problems. In particular for every minimizer v of the quasi-convex functional ess . sup we consider the set suitably defined. If u is an absolute minimizer we give a structure result for A ( u ) and we show that then A ( u ) ⊂ A ( v ) for every minimizer v . Abstract. We discover a new minimality property of the absolute minimizers of supremal functionals (also known as L ∞ Calculus of Variations problems).
我们发现了极限泛函的绝对极小值的一个新的极小性，它的变分问题也称为L∞变分问题。特别是对于拟凸泛函的每一个极小值v。因此，我们认为该集合有适当的定义。如果u是一个绝对最小化器，我们给出a (u)的结构结果，并证明对于每个最小化器v, a (u)∧a (v)。摘要我们发现了极限泛函的绝对极小值的一个新的极小性(也称为L∞变分问题)。
{"title":"A property of Absolute Minimizers in $L^infty$ Calculus of Variations and of solutions of the Aronsson-Euler equation","authors":"Camilla Brizzi, L. Pascale","doi":"10.57262/ade028-0304-287","DOIUrl":"https://doi.org/10.57262/ade028-0304-287","url":null,"abstract":"We discover a new minimality property of the absolute minimizers of supremal functionals, whose variational problems are also known as L ∞ variational problems. In particular for every minimizer v of the quasi-convex functional ess . sup we consider the set suitably defined. If u is an absolute minimizer we give a structure result for A ( u ) and we show that then A ( u ) ⊂ A ( v ) for every minimizer v . Abstract. We discover a new minimality property of the absolute minimizers of supremal functionals (also known as L ∞ Calculus of Variations problems).","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48258026","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}
Pub Date : 2021-06-01DOI: 10.57262/ade026-0708-281
M. Ragusa, Fan Wu
{"title":"Global regularity and stability of solutions to the 3D\u0000 double-diffusive convection system with Navier boundary conditions","authors":"M. Ragusa, Fan Wu","doi":"10.57262/ade026-0708-281","DOIUrl":"https://doi.org/10.57262/ade026-0708-281","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42913223","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}
Pub Date : 2021-06-01DOI: 10.57262/ade026-0708-341
Changmu Chu
{"title":"Positive solutions for a class of $p(x)$-Laplacian equation\u0000 involving concave-convex nonlinearities","authors":"Changmu Chu","doi":"10.57262/ade026-0708-341","DOIUrl":"https://doi.org/10.57262/ade026-0708-341","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45513166","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}
Pub Date : 2021-06-01DOI: 10.57262/ade026-0708-305
J. Restrepo, D. Suragan
{"title":"Direct and inverse Cauchy problems for generalized space-time\u0000 fractional differential equations","authors":"J. Restrepo, D. Suragan","doi":"10.57262/ade026-0708-305","DOIUrl":"https://doi.org/10.57262/ade026-0708-305","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43662150","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}
Pub Date : 2021-04-08DOI: 10.57262/ade026-1112-535
K. Bal, Prashanta Garain, T. Mukherjee
−∆H,pu = λf(x) uq(x) + g(u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, under the assumption Ω is a bounded smooth domain in R with p,N ≥ 2, λ > 0 and 0 < q ∈ C(Ω̄). For the purely singular case that is g ≡ 0, we proved existence and uniqueness of solution. We also demonstrate the existence of multiple solution to (P ) provided f ≡ 1 and g(u) = u for r ∈ (p− 1, p − 1).
{"title":"On an Anisotropic $p$-Laplace equation with variable singular exponent","authors":"K. Bal, Prashanta Garain, T. Mukherjee","doi":"10.57262/ade026-1112-535","DOIUrl":"https://doi.org/10.57262/ade026-1112-535","url":null,"abstract":" −∆H,pu = λf(x) uq(x) + g(u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, under the assumption Ω is a bounded smooth domain in R with p,N ≥ 2, λ > 0 and 0 < q ∈ C(Ω̄). For the purely singular case that is g ≡ 0, we proved existence and uniqueness of solution. We also demonstrate the existence of multiple solution to (P ) provided f ≡ 1 and g(u) = u for r ∈ (p− 1, p − 1).","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49495374","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}
Pub Date : 2021-04-01DOI: 10.57262/ade026-0506-201
Jianqing Chen, Xiuli Tang
{"title":"Least energy solutions to an elliptic system with couplings on Kirchhoff term and nonlinear part","authors":"Jianqing Chen, Xiuli Tang","doi":"10.57262/ade026-0506-201","DOIUrl":"https://doi.org/10.57262/ade026-0506-201","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":"45023329","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}
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：