On some elliptic interface problems with nonhomogeneous jump conditions

Abstract

We obtain nontrivial solutions of some elliptic interface problems with nonhomogeneous jump conditions that arise in localized chemical reactions and nonlinear neutral inclusions. Our proofs in bounded domains use Morse theoretical arguments, in particular, critical group computations. An extension to the whole space is proved using concentration compactness arguments.

Keywords

• elliptic interface problems
• nonhomogeneous jump conditions
• nontrivial solutions
• morse theory
• critical groups
• nonlinear eigenvalue problems
• yang index
• anisotropic problems
• concentration compactness