Existence of infinitelymany solutions for double phase problem with sign-changing potential

被引：21

作者：

Ge, Bin ^{[1
]}

Chen, Zhi-Yuan ^{[2
]}

机构：

[1] Harbin Engn Univ, Sch Math Sci, Harbin 150001, Heilongjiang, Peoples R China

[2] Harbin Engn Univ, Coll Comp Sci & Technol, Harbin 150001, Heilongjiang, Peoples R China

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2019年 / 113卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Double phase problem; Variational method; Multiple solutions; Sign-changing potential; EQUATIONS;

D O I：

10.1007/s13398-019-00684-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the existence of infinitely many solutions for the following double phase problem {- div(|. u| p- 2. u + a(x)|. u| q- 2. u) = f (x, u), in Omega, u = 0, on partial derivative Omega where N = 2 and 1 < p < q < N. Based on a direct sum decomposition of a space W1, H 0 (Omega), we prove that the above problem possesses multiple solutions under mild assumptions on a and f. The primitive of the nonlinearity f is of super- q growth near infinity in u and allowed to be sign- changing. Furthermore, our assumptions are suitable and different from those studied previously.

引用

页码：3185 / 3196

页数：12

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