Three solutions of p-Laplacian equations via a critical point theorem of Ricceri |
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| Authors: | Chun-yan Xue He-yu Xu |
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| Institution: | 1. School of Science, Beijing Information Science and Technology University, Beijing, 100192, China
2. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, China
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| Abstract: | In this paper, we consider the following quasilinear differential equation $(\phi _p (u'))' + \lambda f(t,u) = 0$ subject to one of the two boundary conditions: $u(0) = u'(1) = 0,u'(0) = u(1) = 0$ . After transforming them into a problem of symmetrical solutions, the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri. An example is given to demonstrate our main result. |
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| Keywords: | boundary value problem critical point theorem three solutions symmetrical solution |
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