We study the degenerate semilinear elliptic systems of the form , where is an open bounded domain with smooth boundary , the measurable, nonnegative diffusion coefficients , are allowed to vanish in (as well as at the boundary ) and/or to blow up in . 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.
"Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues." Abstr. Appl. Anal. 2012 (SI11) 1 - 19, 2012. https://doi.org/10.1155/2012/532430