EXISTENCE OF SOLUTIONS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS FOR NONLINEAR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm-Liouville boundary value problems for nonlinear second order impulsive differential equations in Banaeh spaces.     

Oscillation of second‐order perturbed differential equations

We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiple solutions of boundary‐value problems for impulsive differential equations

In this paper, we investigate the existence of multiple solutions to a second‐order Dirichlet boundary‐value problem with impulsive effects. The proof is based on critical point theorems. Copyright © 2011 John Wiley & Sons, Ltd.     

Positive solutions for systems of nonlinear second‐order multipoint boundary value problems

We study the existence of positive solutions for systems of second‐order nonlinear ordinary differential equations, subject to multipoint boundary conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

n阶非线性常微分方程非线性k点边值问题解的存在性

利用格林函数和上下解方法讨论了n阶非线性常微分方程之几类具有非线性k点边界条件的边值问题的存在性。     

Study of singular boundary value problems for second order impulsive differential equations

This paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established.     

Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations

In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed‐point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd.     

Boundary value problems for first order impulsive delay differential equations with a parameter

In this paper, by means of the method of upper and lower solutions and monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established.     

Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations

In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form

Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones.     

高阶非线性阻尼脉冲微分方程解的振动性

研究了一类高阶非线性阻尼脉冲微分方程振动状态,得到振动解的充分条件.     

Studies on anti‐periodic boundary value problems for two classes of special second order impulsive differential equations

We consider anti‐periodic boundary value problems for two classes of special second order impulsive differential equations. On the basis of several important impulsive differential inequalities, by using the monotone iterative technique coupled with lower and upper solutions, we obtain sufficient conditions to guarantee the existence and uniqueness of solutions for such problems. Further, we give two examples to illustrate our conclusions. Copyright © 2013 John Wiley & Sons, Ltd.     

Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations

This paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations

(∗)     

Periodic boundary value problems for impulsive fuzzy differential equations

The peculiarity of the Hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations. In this work, we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method. Fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic ‘linear’ differential problems is also provided.     

Functional impulsive differential equation of order α∈(1,2) with nonlocal initial and integral boundary conditions

The main work is related to show the existence and uniqueness of solution for the fractional impulsive differential equation of order α∈(1,2) with an integral boundary condition and finite delay. Using the application of the Banach and Sadovaskii fixed‐point theorems, we obtain the main results. An example is presented at the end to verify the results of the paper. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence of positive solutions for fourth‐order impulsive integral boundary value problems on time scales

This paper is devoted to the existence of positive solutions for a fourth‐order impulsive boundary value problem with integral boundary conditions on time scales. Existence results of at least two and three positive solutions are established via the double fixed point theorem and six functionals fixed point theorem, respectively. Also, an example is given to illustrate the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Multiple positive solutions for first order impulsive superlinear integro-differential equations on the half line

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.     

Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations

This paper is devoted to study the existence of multiple positive solutions for the second order Dirichlet boundary value problem with impulse effects. The main results here is the generalization of Liu and Li [L. Liu, F.Y. Li, Multiple positive solution of nonlinear two-point boundary value problems, J. Math. Anal. Appl. 203 (1996) 610-625] for ordinary differential equations. Existence is established via the theory of fixed point index in cones.     

Multiple positive solutions of periodic boundary value problems for second order impulsive differential equations

This paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problem with impulse effects. The main results here are the generalization of Jiang [Daqing Jiang, On the existence of positive solutions to second order periodic BVPs, Acta Math. Sci. 18 (1998) 31–35] for ordinary differential equations. Existence is established via the theory of fixed point index in cones.     

Applications of variational methods to Sturm–Liouville boundary‐value problem for fourth‐order impulsive differential equations

In this paper, we study Sturm–Liouville boundary‐value problem for fourth‐order impulsive differential equations. Applying variational methods, several new existence results are obtained. Copyright © 2013 John Wiley & Sons, Ltd.     

Controllability of second‐order impulsive neutral functional differential inclusions in Banach spaces

In this paper, we shall prove the controllability of second‐order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multi‐valued mappings. As an example, we also consider an second‐order impulsive neutral functional differential equation with infinite delay. Copyright © 2009 John Wiley & Sons, Ltd.