Open Access Research

Existence, uniqueness and stability of positive solutions to a general sublinear elliptic systems

Boying Wu1 and Renhao Cui12*

Author Affiliations

1 Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P.R. China

2 Y.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, P.R. China

For all author emails, please log on.

Boundary Value Problems 2013, 2013:74  doi:10.1186/1687-2770-2013-74

Published: 4 April 2013

Abstract

In this paper, we make use of a new stability result and bifurcation theory to study the existence and uniqueness of positive solutions to semilinear elliptic systems with some general sublinear conditions. Moreover, we obtain the precise global bifurcation diagrams of the system in a single monotone solution curve.

MSC: 35J55, 35B32.

Keywords:
semilinear elliptic systems; positive solution; stability; existence; uniqueness