Existence and multiplicity of solutions for a class of ()-Laplacian elliptic system in via genus theory

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• 作者：Liben Wang ; Xingyong Zhang ; ^{zhangxingyong1@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hui Fang
• 关键词：(ϕ1ϕ1 ; ϕ2ϕ2)-Laplacian system ; Genus theory ; Weak solution ; Critical point
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：72
• 期：1
• 页码：110-130
• 全文大小：460 K

文摘

In this paper, we investigate the following nonlinear and non-homogeneous elliptic system involving (ϕ₁,ϕ₂)den">de">$({\varphi }_1,{\varphi }_2)$-Laplacian where the functions V_i(x)(i=1,2)den">de">$V_i\left(x\right)(i=1,2)$ are bounded and positive in R^Nden">de">${\mathbb{R}}^N$, the functions de83567df91" title="Click to view the MathML source">ϕ_i(t)t(i=1,2)den">de">${\varphi }_i\left(t\right)t(i=1,2)$ are increasing homeomorphisms from R⁺den">de">${\mathbb{R}}^{+}$ onto R⁺den">de">${\mathbb{R}}^{+}$, and the function Fden">de">$F$ is of class C¹(R^N+2,R)den">de">$C^1({\mathbb{R}}^{N+2},\mathbb{R})$ and has a sub-linear Orlicz–Sobolev growth. By using the least action principle, we obtain that system has at least one nontrivial solution. When Fden">de">$F$ satisfies an additional symmetric condition, by using the genus theory, we obtain that system has infinitely many solutions.