EXISTENCE OF WEAK NON-NEGATIVE SOLUTIONS FOR A CLASS OF NONUNIFORMLY BOUNDARY VALUE PROBLEM

Title & Authors
EXISTENCE OF WEAK NON-NEGATIVE SOLUTIONS FOR A CLASS OF NONUNIFORMLY BOUNDARY VALUE PROBLEM
Hang, Trinh Thi Minh; Toan, Hoang Quoc;

Abstract
The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation: $\small{-div(h(x){\nabla}u)=f(x,u)\;in\;{\Omega}}$ with Dirichlet boundary condition in a bounded domain $\small{{\Omega}{\subset}\mathbb{R}^N}$, $\small{N{\geq}3}$, where $\small{h(x){\in}L^1_{loc}({\Omega})}$, $\small{f(x,s)}$ has asymptotically linear behavior. The solutions will be obtained in a subspace of the space $\small{H^1_0({\Omega})}$ and the proofs rely essentially on a variation of the mountain pass theorem in [12].
Keywords
mountain pass theorem;the weakly continuously differentiable functional;
Language
English
Cited by
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