Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System
Pure and Applied Mathematics Journal
Volume 2, Issue 6, December 2013, Pages: 179-183
Received: Nov. 11, 2013;
Published: Dec. 10, 2013
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Wang Feng, Jiangsu Union Technical Institute, Yancheng College of Mechatronic Technology, Yancheng, Jiangsu 224005, China
Junmin Zhang, Department of Mathmatics and Applied Mathmatics, Hanshan Normal University, Chaozhou, Guangdong 521041, China
By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.
Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System, Pure and Applied Mathematics Journal.
Vol. 2, No. 6,
2013, pp. 179-183.
Guo Dajun, Lakshmikantham V, Nonlinear problems in abstract cones[M],San Diego: Academic Press,1998, 24-56.
Anuradha V, Hai D, Shivaji R, Existence results for superlin- ear semipositone BVP’s[J], Pro Amer Math Soc, 1996, 124(3): 747-763.
Agarwal R P, O’Regan D, A note on existence of nonnegative solutions to singular semipositone problems[J], Nonlinear Anal, 1999, 36(5): 615-622.
Xu Xian, Positive solutions for singular semipositone boundary value problems[J], J Math Anal Appl, 2002,273(2): 480-491.
Zhang Xinguang, Liu Lishan, Positive solutions of superlinear semipositone singular Dirichlet boundary value problems[J], J Math Anal Appl, 2006, 316(2): 525-537.
Zhang Xinguang, Zhao Zenqin, Positive solution of fourth order singular semipositone boundary value problem[J], J Systems Sci Math Sci, 2006, 26(5): 553-560.
Fink A M, Gatica J A, Positive solutions of second order systems of boundary value problems[J], J Math Anal Appl, 1993, 180(1): 93-108.
Agarwal R P, O’Regan D, A coupled system of boundary value problems[J], Appl Anal, 1998, 69: 381-385.
Xu Xian, Positive solutions for singular semipositone three- point systems[J], Nonlinear Anal, 2007, 66: 791-805.
Liu Lishan, Zhang Xinguang, Wu Yonghong, On existence of positive solutions of a two-point boundary problem for a nonlinear singular semipositone system[J], Appl Math Comput, 2007, 192: 223-232.