The Keller–Osserman-type conditions for the study of a semilinear elliptic system

Abstract

Abstract We study the following system of equations: 0.1 {Δu1=p1(|x|)f1(u1,u2)in RN,Δu2=p2(|x|)f2(u1,u2)in RN. $$ \textstyle\begin{cases} \Delta u_{1}=p_{1} ( \vert x \vert ) f_{1} ( u_{1},u_{2} ) &\text{in }\mathbb{R}^{N}, \\ \Delta u_{2}=p_{2} ( \vert x \vert ) f_{2} ( u_{1},u_{2} )& \text{in }\mathbb{R}^{N}. \end{cases} $$ Here f1 $f_{1}$, f2 $f_{2}$ are continuous nonlinear functions that satisfy Keller–Osserman-type conditions, and p1 $p_{1}$ and p2 $p_{2}$ are continuous weight functions. We establish the existence of radial solutions for this system under various boundary conditions.

Keywords

• Entire solutions
• Large solution
• Systems of elliptic equations