A semilinear elliptic system with vanishing nonlinearities

Pages: 688 - 693, Issue Special, July 2003

 Abstract        Full Text (176.4K)              

Rafael Ortega - Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain (email)
James R. Ward Jr - Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, United States (email)

Abstract: The Neumann boundary value problem is examined for systems of elliptic equations of the form $\Delta u + g(u) = f(x), x \in \omega.$ It is assumed that $g \in 2 C(\mathbb(R)^N,\mathbb(R)^N)$ is a bounded function which may vanish at infinity. Leray-Schauder degree methods are used.

Keywords:  Neumann problem, solutions, existence, bounds, resonance.
Mathematics Subject Classification:  Primary: 35J55, 35J60; Secondary: 47H11.

Received: August 2002;      Revised: February 2003;      Published: April 2003.