an:05072940
Zbl 1104.45003
Li, Fuyi; Li, Yuhua; Liang, Zhanping
Existence of solutions to nonlinear Hammerstein integral equations and applications
EN
J. Math. Anal. Appl. 323, No. 1, 209-227 (2006).
00186813
2006
j
45G10 34B15
strongly monotone operator principle; mountain pass Lemma; linking theorem; fourth-order boundary value problem; nonlinear integral equations; existence of solution; Hilbert space; critical point theory
Authors' abstract: The authors study the existence and multiplicity of solutions of the operator equation \(Kfu=u\) in the real Hilbert space \(L^{2}(G)\). Under certain conditions on the linear operator \(K\), they 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. The quadratic root operator \(K^{1/2}\) and its properties play an important role. As an application, the authors 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.
Yves Cherruault (Paris)