Abstract and Applied Analysis

Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues

Yu-Cheng An and Hong-Min Suo

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We study the degenerate semilinear elliptic systems of the form - div ( h 1 ( x ) u ) = λ ( a ( x ) u + b ( x ) v ) + F u ( x , u , v ) , x Ω , - div ( h 2 ( x ) v ) = λ ( d ( x ) v + b ( x ) u ) + F v ( x , u , v ) , x Ω , u | Ω = v | Ω = 0 , where Ω R N ( N 2 ) is an open bounded domain with smooth boundary Ω , the measurable, nonnegative diffusion coefficients h 1 , h 2 are allowed to vanish in Ω (as well as at the boundary Ω ) and/or to blow up in Ω ¯ . Some multiplicity results of solutions are obtained for the degenerate elliptic systems which are near resonance at higher eigenvalues by the classical saddle point theorem and a local saddle point theorem in critical point theory.

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Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 532430, 19 pages.

First available in Project Euclid: 4 April 2013

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An, Yu-Cheng; Suo, Hong-Min. Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 532430, 19 pages. doi:10.1155/2012/532430. https://projecteuclid.org/euclid.aaa/1365099939

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