Existence of solutions to nonlinear Hammerstein integral equations and applications |
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Authors: | Fuyi Li Yuhua Li Zhanping Liang |
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Institution: | Department of Mathematics, Shanxi University, Taiyuan 030006, People's Republic of China |
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Abstract: | In this paper, we study the existence and multiplicity of solutions of the operator equation Kfu=u in the real Hilbert space L2(G). 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 K1/2 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. |
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Keywords: | Strongly monotone operator principle PS condition Mountain pass lemma Linking theorem Fourth-order boundary value problem |
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