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Existence and uniqueness of positive solutions for singular three-point boundary value problems
Chunmei Miao,Weigao Ge 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, the singular three-point boundary value problem u〃(t) + f(t,u) = 0, t 2 (0, 1), u(0) = 0, u(1) = αu(η), is studied, where 0 < η < 1, α > 0, f(t, u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results. In this paper, the singular three-point boundary value problem u〃(t) + f(t,u) = 0, t 2 (0, 1), u(0) = 0, u(1) = αu(η), is studied, where 0 < η < 1, α > 0, f(t, u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.
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.
Chunmei Miao,Wei-Gao Ge,Zhaojun Zhang 한국수학교육학회 2014 純粹 및 應用數學 Vol.21 No.3
In this paper, we study the existence of positive solutions for singularimpulsive differential equations with integral boundary conditions "( )+ ( ) ( , ( ), '( ))=0, ∊ ',∆ ( )= ( ( ), '( )), =1,2,…, ,∆ '( )=- ( ( ), '( )), =1,2,…, , (0)=∫10 ( ) ( ) , '(1)=0,where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based onthe theory of Leray-Schauder degree, together with a truncation technique. Somerecent results in the literature are generalized and improved.