MULTIPLICITY OF SOLUTIONS FOR BIHARMONIC ELLIPTIC SYSTEMS INVOLVING CRITICAL NONLINEARITY

Title & Authors
MULTIPLICITY OF SOLUTIONS FOR BIHARMONIC ELLIPTIC SYSTEMS INVOLVING CRITICAL NONLINEARITY
Lu, Dengfeng; Xiao, Jianhai;

Abstract
In this paper, we consider the biharmonic elliptic systems of the form $\small{\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},}$, where $\small{{\Omega}{\subset}\mathbb{R}^N}$ is a bounded domain with smooth boundary $\small{{\partial}{\Omega}}$, $\small{{\Delta}^2}$ is the biharmonic operator, $\small{N{\geq}5}$, $\small{2{\leq}q}$ < $\small{2^*}$, $\small{2^*=\frac{2N}{N-4}}$ denotes the critical Sobolev exponent, $\small{F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)}$ is homogeneous function of degree $\small{2^*}$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on $\small{{\lambda}}$ and $\small{{\delta}}$.
Keywords
biharmonic elliptic system;critical Sobolev exponent;variational method;multiple solutions;
Language
English
Cited by
1.
ON A CLASSIFICATION OF WARPED PRODUCT SPACES WITH GRADIENT RICCI SOLITONS, Korean Journal of Mathematics, 2016, 24, 4, 627
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