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

Mohamed Jleli and Bessem Samet
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Mohamed Jleli: Department of Mathematics, College of Science King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Bessem Samet: Department of Mathematics, College of Science King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2019, vol. 7, issue 9, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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