Infinitely many mountain pass solutions on a kind of fourth-order Neumann boundary value problem |
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| Authors: | Yang Yang Jihui Zhang |
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| Institution: | a Institute of Mathematics, School of Mathematics and Computer 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, the existence of infinitely many mountain pass solutions are obtained for the fourth-order boundary value problem (BVP) u(4)(t)-2u″(t)+u(t)=f(u(t)),0<t<1, u′(0)=u′(1)=u?(0)=u?(1)=0, where f:R→R is continuous. The study of the problem is based on the variational methods and critical point theory. We prove the conclusion by using 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 Critical point Mountain Pass Theorem in Order Intervals Morse theory |
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