Existence and multiplicity of positive solutions of nonlinear integral and differential equations.

摘要

In this dissertation, we use a fixed point theorem of cone expansion and compression combined with degree arguments to study the existence, nonexistence and multiplicity of positive solutions for systems of nonlinear integral equations. We obtain, in a unified manner, existence, nonexistence and multiplicity results for positive radial solutions of elliptic systems on an annulus which generalize and extend earlier results. Using the same method we also study existence, nonexistence and multiplicity of a class of integral equations which arise from differential equations with nonlinear boundary conditions.