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

被引：3

作者：

Trinh Thi Minh Hang ^{[1
]}

Hoang Quoc Toan ^{[2
]}

机构：

[1] Hanoi Univ Civil Engn, Dept Informat, Hanoi, Vietnam

[2] Hanoi Univ Sci, Dept Math, Hanoi, Vietnam

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2011年 / 48卷 / 06期

关键词：

Neumann problem; p-Laplacian; Mountain pass theorem; the weakly continuously differentiable functional; MULTIPLICITY;

D O I：

10.4134/BKMS.2011.48.6.1169

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form -div(h(x)vertical bar del u vertical bar(p-2)del u) + b(x)vertical bar u vertical bar(p-2)u = f(x,u), p >= 2 in an unbounded domain Omega subset of R(N), N >= 3, with sufficiently smooth bounded boundary partial derivative Omega, where h(x) is an element of L(loc)(1)((Omega) over bar), (Omega) over bar = Omega boolean OR partial derivative Omega, h(x) >= 1 for all x is an element of Omega. The proof of main results rely essentially on the arguments of variational method.

引用

页码：1169 / 1182

页数：14

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