Existence of solutions for a sublinear system of elliptic equations

Abstract

We study the existence of non-trivial non-negative solutions for the system $$ displaylines{ -Delta u = |x|^av^p cr Delta v = |x|^bu^q,, }$$ where $p$ and $q$ are positive constants with $pq2$) except for the center zero. We look for pairs of functions that satisfy the above system and Dirichlet boundary conditions set to zero. Our results also apply to some super-linear systems.

Keywords

• Semilinear elliptic systems
• sub-harmonic functions
• super-harmonic functions