ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN

Title & Authors
ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN
Hang, Trinh Thi Minh; Toan, Hoang Quoc;

Abstract
In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $\small{-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2}$ in an unbounded domain $\small{{\Omega}{\subset}\mathbb{R}^N}$, $\small{N{\geq}3}$, with sufficiently smooth bounded boundary $\small{{\partial}{\Omega}}$, where $\small{h(x){\in}L_{loc}^1(\overline{\Omega})}$, $\small{\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}}$, $\small{h(x){\geq}1}$ for all $\small{x{\in}{\Omega}}$. The proof of main results rely essentially on the arguments of variational method.
Keywords
Neumann problem;p-Laplacian;Mountain pass theorem;the weakly continuously differentiable functional;
Language
English
Cited by
1.
ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION,;;

대한수학회보, 2014. vol.51. 6, pp.1669-1687
1.
ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION, Bulletin of the Korean Mathematical Society, 2014, 51, 6, 1669
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