Differential and Integral Equations

Existence results for a class of $p$-Laplacian problems with sign-changing weight

Maya Chhetri, Shobha Oruganti, and R. Shivaji

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Consider the boundary-value problem \begin{equation} \begin{array}{c} -\Delta_p u = \lambda g(x)f(u) \quad \mbox{in}\ \Omega \nonumber\\ u=0 \quad \mbox{on}\quad \partial \Omega, \nonumber \end{array} \end{equation} where $\lambda > 0$ is a parameter, $\Omega$ is a bounded domain in $\mathbb R^N,\, N \geq 1,$ with sufficiently smooth boundary $\partial \Omega$ and $\Delta_p u:= div(|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian operator for $p > 1$. Here $g$ is a $C^1$ sign-changing function that may be negative near the boundary and $f $ is a $C^1$ nondecreasing function satisfying $f(0)>0$. We discuss existence results for positive solutions when $f$ satisfies certain additional conditions. We employ the method of sub-super solutions to obtain our results.

Article information

Source
Differential Integral Equations, Volume 18, Number 9 (2005), 991-996.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060118

Mathematical Reviews number (MathSciNet)
MR2162422

Zentralblatt MATH identifier
1212.35147

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J25: Boundary value problems for second-order elliptic equations

Citation

Chhetri, Maya; Oruganti, Shobha; Shivaji, R. Existence results for a class of $p$-Laplacian problems with sign-changing weight. Differential Integral Equations 18 (2005), no. 9, 991--996. https://projecteuclid.org/euclid.die/1356060118


Export citation