Existence and multiplicity of solutions for semilinear elliptic boundary value problems.

摘要

We study the existence, multiplicity, bifurcation and the stability of the solutions to semilinear elliptic boundary value problems. These problems are motivated both by the mathematical structure and the numerous applications in fluid mechanics, chemical reactions, nuclear reactors, Riemannian geometry and elasticity theory. Existence and multiplicity of positive solutions is important because in many applications the solution represents quantities such as concentration or density and hence has to be nonnegative. We consider the problem for different classes of nonlinearities and obtain the existence and multiplicity of positive solutions. For a certain family of problems, we obtain a complete structure for the branches of radial solutions.