Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions | Hindawi Publishing Corporation Boundary Value Problems Volume 2o10 Article ID 862079 23 pages doi 2010 862079 Research Article Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions Xingqiu Zhang1 2 and Yujun Cui3 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 Correspondence should be addressed to Xingqiu Zhang zhxq197508@ Received 7 April 2010 Accepted 12 August 2010 Academic Editor Claudianor O. Alves Copyright 2010 X. Zhang and Y. Cui. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. By employing upper and lower solutions method together with maximal principle we establish a necessary and sufficient condition for the existence of pseudo-C3 0 1 as well as C2 0 1 positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t 0 t 1 and u 0. The dual results for the other integral boundary condition are also given. 1. Introduction In this paper we consider the existence of positive solutions for the following nonlinear fourth-order singular p-Laplacian differential equations with integral boundary conditions Pp x t f t x t x t 0 t 1 x 0 f g s x s ds x 1 0 0 f 1 Pp x 0 pp x 1 h s tpp x s ds 0 2 Boundary Value Problems where pp t t p-2 t p 2 ựq y- 1 p 1 q 1 f e CJ X R X R R J 0 1 R 0 x R 0 x I 0 1 and g h e L1 0 1 is nonnegative. Let Ơ1 J01 1 -s g s ds Ơ2 J01 h s ds. Throughout this paper we always assume that 0 J01 g s ds 1 0 J01 h s ds 1 and nonlinear term f satisfies the following hypothesis H f t u v J X R
