NONLINEAR SPECTRAL THEORY AND OPERATOR EQUATIONS

Abstract

In this paper, the author's theory of nonlinear spectrum is applied to the study of some integral equations involving Urysohn and Hammerstein operators. Results on existence of solutions, bifurcation points, asymptotic bifurcation points are obtained and a generalization of the Borsuk-Ulam theorem is given. The theorems are used to study a second order differential equation under some m-point boundary conditions. The results on the existence of a solution generalize some previous work.