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Existence of infinitely many mountain pass solutions for some fourth-order boundary value problems with a parameter
Authors:Yang Yang  Jihui Zhang
Institution:a Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People’s Republic of China
b School of Science, Jiangnan University, Wuxi, People’s Republic of China
Abstract:In this paper, for the fourth-order boundary value problem (BVP) View the MathML source,0<t<1,u(0)=u(1)=u(0)=u(1)=0, where f:0,1]×RR is continuous, η≤0 is a parameter, the existence of infinitely many mountain pass solutions are obtained with the variational methods and critical point theory. We prove the conclusion by combining sub-sup solution method, Mountain pass theorem in order intervals, Leray-Schauder degree theory and Morse theory.
Keywords:Boundary value problem  Sub-sup solution method  Comparison theorem  Parameter  Variational method
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