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EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR MULTIPOINT BOUNDARY VALUE PROBLEMS
Ji, Dehong,Yang, Yitao,Ge, Weigao The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1
This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian $({\phi}_p(u'))'(t)$ + f(t,u(t)) = 0, $t{\in}$ (0, 1), subject to the boundary value conditions: u'(0) - $\sum\limits^n_{i=1}{\alpha_i}u({\xi}_i)$ = 0, u'(1) + $\sum\limits^n_{i=1}{\alpha_i}u({\eta}_i)$ = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.
Existence and multiplicity of positive solutions for multipoint boundary value problems
Dehong Ji,Yitao Yang,Weigao Ge 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian (φp(u‘))’(t) + f(t, u(t)) = 0, t ∈ (0, 1), subject to the boundary value conditions: <수식>,<수식> Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian (φp(u‘))’(t) + f(t, u(t)) = 0, t ∈ (0, 1), subject to the boundary value conditions: <수식>,<수식> Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.
POSITIVE SOLUTION FOR SYSTEMS OF NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS ON TIME SCALES
Chunmei Miao,Dehong Ji,Junfang Zhao,Weigao Ge,Jiani Zhang 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.4
In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale T [수식] where [수식] and [수식] may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems [수식], and [수식] satisfying similar boundary conditions.