几类分数阶微分方程边值问题的正解的存在性.pdf

?/ ??/ ??/ ??/ ? 300 , . . , : , . . , [12-20], [31-35]. , , . p-Laplacian ????????? cD γ(φ( cD αu(t))) =λf(t, u(t)), 0< t <1, u(0) +u ′(0) = 0, u(1) +u ′(1) = 0, cD αu(t)| t=0= cD αu(t)| t=1= 0, () 1< α, γ≤2,λ>0,f: [0,1]×[0,∞)→[0,∞) ,φ,φ(0) = 0, cD α, cD γ Caputo . , , . ,????? cD αu(t) +f(t, u(t), u ′(t)) = 0, 0< t <1, u(0) =u ′′(0) = 0, u ′(1) = Z1 0 h(t)u(t)dt, () 2< α≤3, cD αα Caputo ,h∈L 1[0,1] ,f: (0,1)×(0,∞)×(?∞,+∞)→[0,∞) . , . i ,????????? D μu(t) =f(t, u(t), u(t?τ)), 0< t <1, u(t) =?(t),?τ≤t≤0, u(1) = 0, () 1< μ≤2, τ>0,f∈C([0,1]×[0,∞)×[0,+∞),(?∞,+∞)),?∈C([?τ,0],[0,∞)), ?(0) = 0, D μ μ Riemann-Liouville . ; ; ; ; ii On the Existence of Positive Solutions of Boundary Value Problems (for Systems) of Fractional Di?erential Equations Abstract Fractional calculus is an area having a long history, its infancy dates back to three hundred years, the beginnings of classical calculus. Fractional di?erential equations is a hot topic in recent years. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scienti?c ?elds such as physics, mechanics, chemistry and engineering, etc. Fractional di?erential equation has been continue to in-depth study by the international munity and the importance of natural science. Fractional di?erential equations has e an important modern mathematics research recent years, fractional di?erential equations have been constantly attention of many scholars; see, for example, [12-20], [31-35]. In this paper, using the cone theory, ?xed point theorem for nonlinear functional methods such as the nonlinear fractional di?erential equation existence of positive solutions for boundary value problems, and obtained some new results. The thesis is divided into there chapters according to contents. Chapter 1 In this section we consider the Fractional Di?erential Equations with Integral Boundary??????? cD γ(φ( cD αu(t))) =λf(t, u(t)