On a Discrete Fractional Boundary Value Problem with Nonlocal Fractional Boundary Conditions

In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green＇s function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii＇s fixed point theorem.     

带有积分边界条件的一阶脉冲微分方程奇异边值问题

利用Schauder′s不动点定理研究带有积分边界条件的一阶脉冲微分方程奇异边值问题,得到正解的存在性结论.其中对应非脉冲情形的相关结论也是新的.     

一类带p-Laplace型算子的高阶两点边值问题的极值解

本文主要研究一类带p-Laplace型算子的n(≥3)阶非线性常微分方程-[φ(u(n-1)(t))]'=f(t,u(t)), a.e.t∈[a,b]满足两点边界条件u(i)(a)=Ai, i＝0,1,…,n-3, u(n-1)(a)=A, u(n-1)(b)=B的边值问题极值解的存在性,这里φ:R→R=(-∞,+∞)是递增的同胚,f:[a,b]×R→R是L 1-Carathéodory函数,A,B,Ai,Bi∈R,i=0,1,…,n-3.主要利用基于反极大值原理的单调迭代方法,得到了上述边值问题极值解的存在性结果.     

分数阶微分方程多点分数阶边值问题

研究分数阶微分方程多点分数阶边值问题解的存在性与唯一性,利用不动点定理,得到了边值问题存在唯一解和至少存在1个解的充分条件.     

Boundary Value Problem for a First-Order Partial Differential Equation with Liouville Fractional Derivative

Differential Equations - We consider a first-order partial differential equation with a fractional derivative with respect to one of two independent variables. Fractional differentiation is given...     

Constructive Method for Solving a Boundary Value Problem with Impedance Boundary Condition for the Helmholtz Equation

We substantiate the collocation method for the singular integral equation of a boundary value problem with impedance condition for the Helmholtz equation. We construct a sequence converging to the exact solution of the original problem and estimate the error.     

非线性分数阶脉冲微分方程边值问题的解

通过Schauder不动点定理和Banach压缩映射原理得到了一类非线性分数阶脉冲微分方程边值问题解的存在性和唯一性结果.     

一类分数阶微分方程正解的存在性

研究了非线性项可变号的分数阶微分方程两点边值问题其中f:[0,1]×[0,∞)→（→∞,∞）是连续的,λ>0,q（t）>0₂通过构造适当算子,继而运用锥上的不动点定理,得到了该问题至少一个正解的存在性.     

Triple Positive Solutions for a Class of Fractional Boundary Value Problem System

In this paper, the solvability for the following fractional boundary value problem system

is studied, where ， are continuous, are the Caputo fractional derivatives, and are the Riemann-Liouville fractional derivatives. The fixed point theorem is used to prove that there are three positive solutions to problems.     

Density of the Extremal Solutions for a Class of Second Order Boundary Value Problem

In this paper, we prove a theorem on the existence of extremal solutions to a second-order differential inclusion with boundary conditions, governed by the subdifferential of a convex function. We also show that the extremal solutions set is dense in the solutions set of the original problem.     

Existence Results for Certain Multi-Orders Impulsive Fractional Boundary Value Problem

We derive in this paper some new existence and uniqueness results for a nonlinear multi-orders impulsive differential equation subject to fractional multi-point fractional integral boundary conditions. The obtained results are based on the Banach’s contraction theorem as well as Schauder fixed point theorem. Finally, two illustrative examples are given.     

Sturm-Liouville算子方程边值问题的最小极值解

利用 Banach空间中度量广义逆理论 ,证明了 LP(a,b)空间中 Sturm-Liouville算子方程边值问题最小极值解的存在性 ,并借助 Banach空间几何方法给出了最小极值解存在的等价条件     

一类二阶非线性常微分方程非线性边界条件的两点边值问题

本文讨论了一类二阶非线性常微分方程之具有线性边界条件的和具有非线性边界条件的两点边值问题解的存在性.     

分数阶p-Laplacian边值问题正解的存在唯一性

运用Schauder不动点定理和上下解方法研究了一类分数阶p-Laplacian边值问题正解的存在性和唯一性,并给出了唯一解的迭代序列.     

Boundary Value Problem for a Linear Ordinary Differential Equation with a Fractional Discretely Distributed Differentiation Operator

The boundary value problem with Robin conditions has been solved for a linear ordinary differential equation with a fractional discretely distributed differentiation operator. The Green function has been constructed.     

Multiplicity of Solutions to Nonlinear Boundary Value Problem with Nonlocal Boundary Condition

In this paper the author considers the following nonlinear boundary value problem with nonlocal boundary conditions $[\left\{ \begin{array}{l} Lu \equiv - \sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial {x_i}}}({a_{ij}}(x)\frac{{\partial u}}{{\partial {x_j}}}) = f(x,u,t)} \u{|_\Gamma } = const, - \int_\Gamma {\sum\limits_{i,j = 1}^n {{a_{ij}}\frac{{\partial u}}{{\partial {x_j}}}\cos (n,{x_i})ds = 0} } \end{array} \right.\]$ Under suitable assumptions on f it is proved that there exists $t_0\in R,-\infinityt_0, at least one solution at t=t_0 at least two solutions as t相似文献   

Existence and Non-existence of Positive Solutions for a Discrete Fractional Boundary Value Problem

In this work, we deal with two-point boundary problem for a finite nabla fractional difference equation. First, we establish an associated Green''s function and state some of its properties. Under suitable conditions, we deduce the existence and non-existence of positive solutions to the considered problem. Finally, we construct a few examples to illustrate the established results.