Mathematical Sciences: Some Semilinear Elliptic Problems

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Abstract DMS-9622102 Wang This proposal is concerned with problems of the existence, qualitative properties, and multiplicity of solutions as well as bifurcation branches of solutions for some model equations of nonlinear elliptic problems including a nonlinear Neumann problem and a semilinear Schrodinger equation. Using these model equations we shall develop some general and systematic methods and approaches which can be used for more general problems. The proposal will use variational and topological techniques to develop analytical results for the problems concerned. Partial differential equations form a basis for mathematical modeling of the physical world. The problems in the proposal arise from a variety of areas of applied sciences. The role of mathematical analysis is to provide qualitative and quantitative information about the solutions, answering questions about uniqueness, multiplicity, shape and growth.