Some Remarks on a Class of Nonuniformly Elliptic Equations of p-Laplacian Type

被引：9

作者：

Ngo, Quoc-Anh ^{[1
,2
]}

Toan, Hoang Quoc ^{[1
]}

机构：

[1] Vietnam Natl Univ, Coll Sci, Dept Math, Hanoi, Vietnam

[2] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

ACTA APPLICANDAE MATHEMATICAE | 2009年 / 106卷 / 02期

关键词：

p-Laplacian; Nonuniform; Landesman-Laser; Elliptic; Divergence form; Landesman-Laser type; SOLVABILITY; RESONANCE;

D O I：

10.1007/s10440-008-9291-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the existence of weak solutions in W-0(1)(Omega) to a class of elliptic problems of the form -div(a(x, del u)) = lambda(1)vertical bar u vertical bar(p-2) u + g(u) - h in a bounded domain Omega of R-N. Here a satisfies vertical bar a(x, xi)vertical bar <= c(0) (h(0) (x) + h(1)(x) vertical bar xi vertical bar(p-1)) for all xi is an element of R-N, a.e. x is an element of Omega, h(0) is an element of Lp/p-1 (Omega), h(1) is an element of L-loc(1) (Omega), h(1) (x) >= 1 for a.e. x in Omega; lambda(1) is the first eigenvalue fro -Delta(p) on Omega with zero Dirichlet boundary condition and g, h satisfy some suitable conditions.

引用

页码：229 / 239

页数：11

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