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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohamed Jleli & Bessem Samet, 2019. "A Lyapunov-Type Inequality for a Laplacian System on a Rectangular Domain with Zero Dirichlet Boundary Conditions," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:850-:d:267227
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