Multiple solutions for fourth-order boundary value problem |
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| Authors: | Changci Pang Wei Dong |
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| Affiliation: | a School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China
b Hebei University of Engineering, Handan, Hebei 056021, China |
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| Abstract: | In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions. |
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| Keywords: | Fixed point index Leray-Schauder degree Fourth-order two point boundary value problem Multiple solutions Sign-changing solutions |
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