Existence of positive solutions for a semilinear elliptic system

Zhitao Zhang, Xiyou Cheng

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.

Keywords


Positive solutions; elliptic system; fixed point index

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