MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR NONLINEAR FRACTIONAL ELLIPTIC EQUATIONS WITH STEEP POTENTIAL

被引：9

作者：

Peng, Song ^{[1
]}

Xia, Aliang ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2018年 / 17卷 / 03期

关键词：

Fractional Laplacian; steep potential; Nehari manifold; concave-convex term; POSITIVE SOLUTIONS; SCHRODINGER-EQUATIONS; NEHARI MANIFOLD; STATES;

D O I：

10.3934/cpaa.2018058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we prove the existence, multiplicity and concentration of non-trivial solutions for the following indefinite fractional elliptic equation with concave-convex nonlinearities: {(-Delta)(alpha)u + V-lambda(x)u = a(x)vertical bar u vertical bar(q-2)u + b(x)vertical bar u vertical bar(p-2)u in R-N, u >= 0 in R-N, where 0 < alpha < 1, N > 2 alpha, 1 < q < 2 < p < 2(alpha)*; with 2(alpha)*= 2N/(N - 2 alpha), the potential V-lambda(x) = lambda V+(x)- V-(x) with V-+/- = max{+/- V, 0} and the parameter lambda > 0. Our multiplicity results are based on studying the decomposition of the Nehari manifold.

引用

页码：1201 / 1217

页数：17

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