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http://dx.doi.org/10.4134/BKMS.2012.49.4.737

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

Hang, Trinh Thi Minh (Department of Informatics Hanoi University of Civil Engineering)
Toan, Hoang Quoc (Department of Mathematics Hanoi University of Science)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 737-748 More about this Journal
Abstract
The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation: $$-div(h(x){\nabla}u)=f(x,u)\;in\;{\Omega}$$ with Dirichlet boundary condition in a bounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, where $h(x){\in}L^1_{loc}({\Omega})$, $f(x,s)$ has asymptotically linear behavior. The solutions will be obtained in a subspace of the space $H^1_0({\Omega})$ and the proofs rely essentially on a variation of the mountain pass theorem in [12].
Keywords
mountain pass theorem; the weakly continuously differentiable functional;
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