Three positive solutions for multipoint one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative

Authors:
Bo Sun;Weigao Ge;Dongxia Zhao
Affiliations:
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

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Abstract

By applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions for the one-dimensional p-Laplacian differential equation, (@f"p(u^'(t)))^'+q(t)f(t,u(t),u^'(t))=0,t@?(0,1), subject to the following multipoint boundary condition, u^'(0)=@?i=1n@a"iu^'(@x"i),u(1)=@?i=1n@b"iu(@x"i), where @f"p(s)=|s|^p^-^2s with p1. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly.