EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A CLASS OF NONLINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATIONS WITH DELAY

A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO NONLINEAR DELAY FRACTIONAL DIFFERENTIAL EQUATIONS

Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY

Using a fixed point method, in this paper we discuss the existence and uniqueness of positive solutions to a class system of nonlinear fractional differential equations with delay and obtain some new results.     

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.     

时滞微分方程和脉冲时滞微分方程解的存在唯一性

本文研究了时滞微分方程的问题.利用上下解作为耦合初始迭代得到一个收敛于此方程解的单调序列的方法,获得了时滞方程和脉冲时滞微分方程解的存在唯一性结果,推广了文献[3,5]的相关结果.     

EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional differential equations of order q (1 < q ≤ 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.     

EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY

This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.     

EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.     

EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role.     

非线性Kawahara方程解的存在唯一性

非线性Ｋａｗａｈａｒａ方程是描述不同介质中存在单色非线性扰动时长波的传播问题的一类重要物理模型．本文通过对相应线性问题基本解的估计,导出了一类一般的Ｓｔｒｉｃｈａｒｔｚ－型光滑时空混合范数估计,进而得到了非线性Ｋａｗａｈａｒａ方程解的存在唯一性结果．     

非线性Kawahara方程解的存在唯一性

非线性Kawahara方程是描述不同介质中存在单色非线性扰动时长波的传播问题的一类重要物理模型.本文通过对相应线性问题基本解的估计,导出了一类一般的Strichartz-型光滑时空混合范数估计,进而得到了非线性Kawahara方程解的存在唯一性结果.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEM

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.     

三阶非线性常微分方程非线性两点边值问题解的存在性与唯一性

本文得用Ｂｏｌｚａｎｏ定理，给出了三阶非线性常微分方程具非线性两点边界条件的边值问题（１）（２）存在解与存在唯一解的一般结果，并将所得结果应用于Ｌｉｐｓｃｈｉｔｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足（２），（３）的边值问题给出了解存在与存在唯一解的较具体的充分条件。     

一类中立型泛函微分方程周期解的存在性与唯一性

利用Schauder不动点理论,引入线性变换,用逆变换的思想,定性与定量地研究一类中立型泛函微分方程周期解的问题,获得了这一类泛函微分方程周期解存在性与唯一性的充分条件.我们的研究方法异于相关文献中常用的方法.     

CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

A class of second order nonlinear differential equations with delay depengingon the unknown function of the from(r(t)ψ(x(t))x' (t))' f (t, x(t), x (△ (t, x(t)))) = 0in the case where ∫∞0 ds/r(s) ＜∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.     

一类非线性渗流方程Cauchy问题弱解的存在唯一性

讨论具强非线性源和对流项的一般渗流方程以Ｒ＾Ｎ中某一Ｒａｄｏｎ测度为初始迹的Ｃａｕｃｈｙ问题弱解的存在唯一性。     

OSCILLATION FOR A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS WITH NONLINEAR NEUTRAL TERM

By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous literatures.     

EXISTENCE OF POSITIVE MULTIPLE SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR

In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.