The Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem with p-Laplacian

This paper deals with the multiplicity results of positive solutions of one-dimensional singular p-Laplace equation (jp(u'(t)))'+a(t)f(t,u(t),u'(t))=0, 01. By using the Avery-Peterson fixed point theorem, sufficient conditions for the existence of at least three positive solutions to the boundary value problem mentioned above are obtained.

Anahtar Kelimeler:

p-Laplacian; Avery-Peterson fixed-point theorem; positive solution; boundary value problem

The Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem with p-Laplacian

Keywords:

p-Laplacian; Avery-Peterson fixed-point theorem; positive solution; boundary value problem,

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Multiple positive solutions for some p-Laplacian boundary value problems, Appl.Math.Comput. 187(2), 1315-1325 (2007).
Dehong, J., and Weigao, G.: Existence of multiple positive solutions for Sturm-Liouville-like four-point boundary value problem with p-Laplacian,Nonl. Anal. 68, 2638-2646 (2008).
Dexiang, M., J., Han, and Xuegang, Chen: Positive solutions of three-point boundary value problem for the one- dimensional p-Laplacian with singularities,J.Math.Anal.Appl. 324, 118-133 (2006).
Dongxia, Z., Hongzhou, W., and Weigao, G.: Existence of triple positive solutions to a class of p-Laplacian boundary value problems, J.Math.Anal.Appl. 328, 972-983 (2007).
Ming, X., and Shaorong, W.: The existence of positive solution for the one-dimensional p-Laplacian, Acta Mathematica Sinica,(Chinese Series) 49, 162-168 (2006).
Xiangfeng, L.: Multiple positive solutions for some four-point boundary value problems with p-Laplacian , Appl.Math.Comput. 202(1) 413-426 (2008).
Youyu, W., and Weigao, G.: Multiple positive solutions for multipoint boundary value problems with one- dimensional p-Laplacian, J.Math.Anal.Appl. 327, 1381-1395 (2007).
Zhanbing, B., and Weigao, G.: Existence of three positive solutions for the one-dimensional p-Laplacian, Acta Mathematica Sinica,(Chinese Series) 49, 1045-1052 (2006).
Zhanbing, B., Zhanji, G., and Weigao, G.: Multiple positive solutions for some p-Laplacian boundary value problems, J.Math.Anal.Appl. 300, 477-490 (2004).
Zhiyan, L., Shulin, Y., and Weigao, G.: Multiple positive solutions to a nonlinear two-point boundary value problem with p-Laplacian, J.Math.Research and Exposition, 26, 480-488 (2006). Xiang-feng LI
Department of Mathematics, Longdong University, Gansu,Qingyang 745000, P.R. of CHINA e-mail: lxf66006@sina.com Pei-hao ZHAO
Department of Mathematics, Lanzhou University, Gansu, Lanzhou 730000, P. R. of CHINA e-mail: zhaoph@lzu.edu.cn