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

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

Abstract: 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, 0<t<1 subject to the nonlinear boundary conditions ajp(u(0))-bjp(u'(x))=0, gjp(u(1))+djp(u'(h))=0, where jp(x)=|x|p-2x, p>1. 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.

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

Turk. J. Math., 33, (2009), 131-142.
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Other articles published in the same issue: Turk. J. Math.,vol.33,iss.2.