Positive solutions of two-point boundary value problems for fractional singular differential equations

For nonlinear fractional differential equations with singularities in the phase variable, we establish tests for the existence of several positive solutions of two-point boundary value problems.     

Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations

In this work, we investigate existence and uniqueness of solutions for a class of nonlinear multi-point boundary value problems for fractional differential equations. Our analysis relies on the Schauder fixed point theorem and the Banach contraction principle.     

分数阶微分方程m点边值共振问题解的存在性

利用Mawhin延拓定理考察了一类分数阶微分方程m点边值共振问题解的存在性.得到了解的存在性的一个充分性条件,并且举出实例用以说明主要结果.     

Existence results for $$$$-type nonlocal integral boundary value problems for coupled systems of fractional differential equations at resonance

In this paper, a coupled system of \((n-1,1)\)-type nonlinear fractional differential equations with nonlocal integral boundary conditions is considered. The existence of solutions is obtained by means of the coincidence degree theory due to Mawhin.     

Existence of solutions of initial value problems for nonlinear fractional differential equations

In this paper, by using the Schauder fixed point theorem, we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and obtain some new results.     

具有逐项分数阶导数的微分方程边值问题解的存在性

研究了一类具有逐项分数阶导数的微分方程边值问题.对参数的各种取值情况进行了全面的分析,运用Banach压缩映射原理和Schauder不动点定理,得到并证明了边值问题解的存在性定理.最后,给出了两个例子来证明结论有效.     

Positive solutions for multi-point boundary value problems for nonlinear fractional differential equations

The paper studies the problem of existence of positive solution to the following boundary value problem: $D_{0^ + }^\sigma u''(t) - g(t)f(u(t)) = 0$ , t ∈ (0, 1), u″(0) = u″(1) = 0, au(0) ? bu′(0) = Σ _i=1 ^m?2 a _i u(ξ _i ), cu(1) + du′(1) = Σ _i=1 ^m?2 b _i u(ξ _i ), where $D_{0^ + }^\sigma$ is the Riemann-Liouville fractional derivative of order 1 < σ ≤ 2 and f is a lower semi-continuous function. Using Krasnoselskii’s fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is established.     

Existence of solutions for nonlinear boundary value problems of impulsive differential equations

With the help of the coincidence degree continuation theorem, we generalize to the case of impulsive systems of the second order some existence results obtained by Gaines and Mawhin in the ordinary case. In particular, for the impulsive functions the treatment does not assume any monotonicity conditions, which are necessary in earlier papers treated by S.Hu and V.Lakshmikantham, L.H.Erbe and X.Liu with other methods.     

Solutions of two-point boundary value problems for even-order differential equations

The existence of solutions of the two-point boundary value problems consisting of the even-order differential equations

     

Existence of positive solutions for three-point boundary value problems at resonance

With the help of the theorem of a fixed point index for A-proper semilinear operators established by Cremins, we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three-point boundary value problems at resonance.     

Existence of solutions of boundary value problems for second order functional differential equations

In this paper, we deal with the boundary value problem

     

Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations

In this paper, by using the fixed point theory, we study the existence and uniqueness of initial value problems for nonlinear fractional differential equations and obtain a new result.