The Neumann Problem for a Degenerate Elliptic System Near Resonance

Abstract

This paper studies the following system of degenerate equationsand ] is the exterior normal vector on Ω. The coefficient function may vanish in Ω, ∈ (Ω) with > /(2 − ), > /2. We show that the eigenvalues of the operator −div( ( )∇ ) + ( ) are discrete. Secondly, when the linear part is near resonance, we prove the existence of at least two different solutions for the above degenerate system, under suitable conditions on ℎ 1 , ℎ 2 , 1 , and 2 .