A Lyapunov-Type Inequality for a Laplacian System on a Rectangular Domain with Zero Dirichlet Boundary Conditions

Abstract

We consider a coupled system of partial differential equations involving Laplacian operator, on a rectangular domain with zero Dirichlet boundary conditions. A Lyapunov-type inequality related to this problem is derived. This inequality provides a necessary condition for the existence of nontrivial positive solutions.

Keywords

• Lyapunov-type inequality
• coupled system
• Laplacian
• rectangular domain