Multiple positive solutions for singular Quasilinear multipoint BVPs with the first-order derivative

Authors:
Weihua Jiang;Bin Wang;Yanping Guo
Affiliations:
College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, China and College of Mathematics and Science of Information, Hebei Normal University, Shijiazhuang, Hebei, Chi ...;Department of Basic Courses, Hebei Professional and Technological College of Chemical and Pharmaceutical Engineering, Shijiazhuang, Hebei, China;College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, China
Venue:
Boundary Value Problems
Year:
2008

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Abstract

The existence of at least three positive solutions for differential equation (φp(u′(t)))′ + g(t)f(t, u(t), u′(t)) = 0, under one of the following boundary conditions: u(0) = Σi=1m-2 aiu(ξi), ϕp(u′(1)) = Σi=1m-2 biϕp(u′(ξi)) or ϕp(u′(0)) = Σi=1m-2 aiϕp(u′(ξi)), u(1) = Σi=1m-2biu(ξi), is obtained by using the H. Amann fixed point theorem, where ϕp(s) = |s|p-2s, p 1, 0 1 2 m-2 ai 0, bi 0, 0 i=1m-2ai i=1m-2bi g(t) may be singular at any point of [0,1] and f may be noncontinuous.