Differential and Integral Equations

An existence result for a class of superlinear $p$-Laplacian semipositone systems

Abstract

In this paper we study positive solutions for the system \begin{align*} -(r^{N-1}\phi(u'))' & \, =\, \lambda r^{N-1}f(v);\ a\, <\,r\, <\,b; \\ -(r^{N-1}\phi(v'))' & \, =\, \lambda r^{N-1}g(u);\ a\, <\,r\, <\,b; \\ u(a)\, =\, 0 & \,=\,u(b)\,;\, v(a)\,=\,0\,=\,v(b), \end{align*} where $\lambda > 0$ is a parameter and $\phi$ is an odd, increasing homeomorphism on $\Bbb R$. Here $f,\, g \in C[0,\infty)$ belong to a class of superlinear functions at $\infty$. In particular we allow $f(0)$ or $g(0)$ or both to be negative (semipositone system). We discuss the existence of a positive solution for $\lambda$ small. Our proof is based on degree theory.

Article information

Source
Differential Integral Equations, Volume 14, Number 2 (2001), 231-240.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123354

Mathematical Reviews number (MathSciNet)
MR1797388

Zentralblatt MATH identifier
1046.34043

Citation

Hai, D. D.; Shivaji, R.; Maya, C. An existence result for a class of superlinear $p$-Laplacian semipositone systems. Differential Integral Equations 14 (2001), no. 2, 231--240. https://projecteuclid.org/euclid.die/1356123354