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
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
收藏
页码:6287 / 6304
页数:18
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