Existence of solutions to nonlinear Hammerstein integral equations and applications

Abstract: In this paper, we study the existence and multiplicity of solutions of the operator equation in the real Hilbert space . Under certain conditions on the linear operator K, we establish the conditions on f which are able to guarantee that the operator equation has at least one solution, a unique solution, and infinitely many solutions, respectively. The monotone operator principle and the critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role. As an application, we investigate the existence and multiplicity of solutions to fourth-order boundary value problems for ordinary differential equations with two parameters, and give some new existence results of solutions. [Copyright &y& Elsevier]