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

Abstract

The existence, stability and uniqueness of positive solutions to a semilinear elliptic system with sublinear nonlinearities are proved. It is shown that the precise global bifurcation diagram of the positive solutions is a monotone curve with different asymptotical behaviour according to the form of the nonlinearities. Equations with Hölder continuous nonlinearities are also considered.

On the uniqueness and structure of solutions to a coupled elliptic system

“…We also mention that result like Theorem 1.1 can be proved using other method even for a general bounded domain, see [9], but our main emphasis here is to present a systematic approach for radially symmetric solutions and obtain a complete structure of solutions to the shooting problem (1.3), that is information not provided in [9]. We also mention that the shooting problem like (1.3) can be solved numerically, and bifurcation diagrams showing the regions of different types of solutions as in Theorems 1.3 and 1.4 can be numerically obtained [17].…”