The existence of solutions to certain quasilinear elliptic equations

被引：0

作者：

Kuo, Tsang-Hai ^{[1
]}

Chen, Yi-Jung ^{[2
]}

机构：

[1] Chang Gung Univ, Ctr Gen Educ, Tao Yuan, Taiwan

[2] Tamkang Univ, Dept Math, Tamsui, Taiwan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 04期

关键词：

Quasilinear elliptic equation; W(2; p)-estimate; p)(Omega) boolean AND W(0)(1; p)(Omega); solution;

D O I：

10.1016/j.na.2010.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Lu = -Sigma(N)(i,j)(=1) a(ij)(x, u)D(ij)u + c(x, u)u. Consider the quasilinear elliptic equation Lu = f (x, u, del u) on a bounded smooth domain Omega in R(N), where c(x, r) = alpha > 0, f (x, r,xi) = o[vertical bar r vertical bar + h(vertical bar r vertical bar)vertical bar xi vertical bar(2)]. It is shown that if the oscillation of a(ij)(x, r) with respect to r is sufficiently small, then there exists a solution u is an element of W(2,p)(Omega) boolean AND W(0)(1,p) (Omega) to the equation Lu = f (x, u,del u). (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1286 / 1289

页数：4

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