Existence of infinitely many mountain pass solutions for some fourth-order boundary value problems with a parameter |
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| Authors: | Yang Yang Jihui Zhang |
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| 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 |
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| Abstract: | In this paper, for the fourth-order boundary value problem (BVP)  ,0<t<1,u(0)=u(1)=u″(0)=u″(1)=0, where f:0,1]×R→R 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. |
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| Keywords: | Boundary value problem Sub-sup solution method Comparison theorem Parameter Variational method |
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