Topological Methods in Nonlinear Analysis

Existence of positive solutions for a semilinear elliptic system

Zhitao Zhang and Xiyou Cheng

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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.

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

First available in Project Euclid: 20 April 2016

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Zhang, Zhitao; Cheng, Xiyou. Existence of positive solutions for a semilinear elliptic system. Topol. Methods Nonlinear Anal. 37 (2011), no. 1, 103--116.

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