ON A CLASS OF NON-LOCAL ELLIPTIC EQUATIONS WITH ASYMPTOTICALLY LINEAR TERM

被引：5

作者：

Wei, Yuanhong ^{[1
]}

Su, Xifeng ^{[2
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, 19 XinJieKouWai St, Beijing 100875, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Non-local operator; variational method; fractional Laplacian; multiplicity; FRACTIONAL LAPLACIAN; DISLOCATION DYNAMICS; MINIMAL-SURFACES; OBSTACLE PROBLEM; REGULARITY; OPERATORS; DIMENSION; BOUNDARY; CRYSTALS; CONCAVE;

D O I：

10.3934/dcds.2018154

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the nonlinear elliptic PDE driven by the fractional Laplacian with asymptotically linear term. Some results regarding existence and multiplicity of non-trivial solutions are obtained. More precisely, information about multiple non-trivial solutions is given under some hypotheses of asymptotically linear condition; non-local elliptic equations with combined nonlinearities are also studied, and some results of local existence and global existence are obtained. Finally, an L-infinity regularity result is also given in the appendix, using the De Giorgi-Stampacchia iteration method.

引用

页码：6287 / 6304

页数：18

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