Ground state solution for a periodic p&q-Laplacian equation involving critical growth without the Ambrosetti-Rabinowitz condition

被引：1

作者：

Shen, Liejun ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua, Zhejiang, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 09期

关键词：

Ambrosetti-Rabinowitz condition; compactness-concentration principle; critical; ground state solution; p&q-Laplacian equation; Q ELLIPTIC PROBLEMS; POSITIVE SOLUTIONS; NONTRIVIAL SOLUTIONS; EXISTENCE; (P; MULTIPLICITY; Q)-LAPLACIAN;

D O I：

10.1002/mma.9135

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the ground state solutions for the following p & q-Laplacian equation {-delta(p)u - delta(q)u + V(x)(|u|(p-2)u + |u|(q-2)u) =lambda K(x)f(u) + |u|(q & lowast;-2)u, x is an element of R-N,u is an element of W-1,W-p(RN) & cap; W-1,W-q(R-N), where lambda > 0 is a parameter large enough, delta(r)u = div(|& nabla;u|(r-2)& nabla;u) with r is an element of {p, q} denotes the r-Laplacian operator, 1 < p < q < N and q(& lowast;) = Nq/(N - q). Under some assumptions for the periodic potential V, weight function K and non linearity f without the Ambrosetti-Rabinowitz condition, we show the above equation has a ground state solution.

引用

页码：10499 / 10511

页数：13

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