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Existence and Multiplicity of Positive Solutions for a Fourth-Order P-Laplace Equations

Authors:	Zhan-bing Bai

Institution:	Department of Applied Mathematics, Petroleum UniversityEast China Dongying, Shandong 257061, P R China

Abstract:	The solvability of one dimensional fourth-order p-Laplace equations of the type $\left\{ \begin{gathered} \left( {g\left( {u\prime \prime } \right)} \right)\prime \prime + \lambda a\left( t \right)u = 0,{\text{ }}0 < t < 1, \hfill \\ u\left( 0 \right) = u\left( 1 \right) = u\prime \prime \left( 0 \right) = u\prime \prime \left( 1 \right) = 0, \hfill \\ \end{gathered} \right.$ , where, g(v) \| v \|^p–2 v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.

Keywords:	p_Laplacian positive solution cone
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