Open Access Research Article

Positive Solutions for Fourth-Order Singular -Laplacian Differential Equations with Integral Boundary Conditions

Xingqiu Zhang12* and Yujun Cui3

Author Affiliations

1 Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

2 Department of Mathematics, Liaocheng University, Liaocheng, Shandong 252059, China

3 Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266510, China

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Boundary Value Problems 2010, 2010:862079  doi:10.1155/2010/862079

Published: 19 August 2010

Abstract

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo- as well as positive solutions for fourth-order singular -Laplacian differential equations with integral boundary conditions. Our nonlinearity may be singular at , , and . The dual results for the other integral boundary condition are also given.