In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations： Dqu（t） ＋ f（t, u（t）） = 0, 0 t 1, u（0） = 0, u（1）...In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations： Dqu（t） ＋ f（t, u（t）） = 0, 0 t 1, u（0） = 0, u（1） =sum （μiDpu（t）｜t = ξi ） from i =1 to ∞ m-2, where q ∈R , 1 q ≤2 , 0 ξ1 ξ2 ··· ξm-2 ≤ 1/2 , μi ∈[0 , ＋∞） and p = q-1/2 , Γ（q） sum （μiξi（q-1）/2 Γ（（ q＋1）/2） from i =1 to ∞ m-2,Dq is the standard Riemann-Liouville differentiation, and f ∈C （[0 , 1]×[0 , ＋∞） , [0 , ＋∞））. By using the Leggett-Williams fixed point theorem on a convex cone, some multiplicity results of positive solutions are obtained.展开更多
In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order d...In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained.展开更多
基金supported by Hunan Provincial Natural Science Foundation of China(11JJ3009)supported by the Scientific Research Foundation of Hunan Provincial Education Department(11C1187)the Construct Program of the Key Discipline in Hunan Province
文摘In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations： Dqu（t） ＋ f（t, u（t）） = 0, 0 t 1, u（0） = 0, u（1） =sum （μiDpu（t）｜t = ξi ） from i =1 to ∞ m-2, where q ∈R , 1 q ≤2 , 0 ξ1 ξ2 ··· ξm-2 ≤ 1/2 , μi ∈[0 , ＋∞） and p = q-1/2 , Γ（q） sum （μiξi（q-1）/2 Γ（（ q＋1）/2） from i =1 to ∞ m-2,Dq is the standard Riemann-Liouville differentiation, and f ∈C （[0 , 1]×[0 , ＋∞） , [0 , ＋∞））. By using the Leggett-Williams fixed point theorem on a convex cone, some multiplicity results of positive solutions are obtained.
基金Supported by the Scientific Research Foundation of Hunan Provincial Education Department(08C826) was also supported by the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province,and the Construct Program of the Key Discipline in Hunan Province.Supported by the National Natural Science Foundation of China(No.i0531050)the innovation group funds (10621101)973 Program of MOST(2006CB805903)
文摘In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained.
