Topological Methods in Nonlinear Analysis

Existence of positive solutions for a semilinear elliptic system

Zhitao Zhang and Xiyou Cheng

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Abstract

In this paper, we are concerned with the existence of (component-wise) positive solutions for a semilinear elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing a cone $K_1 \times K_2$ which is the Cartesian product of two cones in space $C(\overline{\Omega})$ and computing the fixed point index in $K_1 \times K_2$, we establish the existence of positive solutions for the system. It is remarkable that we deal with our problem on the Cartesian product of two cones, in which the features of two equations can be exploited better.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 37, Number 1 (2011), 103-116.

Dates
First available in Project Euclid: 20 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461181490

Mathematical Reviews number (MathSciNet)
MR2839519

Zentralblatt MATH identifier
1234.35092

Citation

Zhang, Zhitao; Cheng, Xiyou. Existence of positive solutions for a semilinear elliptic system. Topol. Methods Nonlinear Anal. 37 (2011), no. 1, 103--116. https://projecteuclid.org/euclid.tmna/1461181490


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