In this paper, we obtain new oscillation criteria for second-order half-linear impulsive differential equations having fixed moments of impulse actions. We also generalize the results to nonlinear impulsive equations. The oscillation criteria obtained in this paper can be considered as extensions of those given by Leighton, (J. London Math. Soc. 27 (1952)), Coles (Proc. Amer. Math. Soc. 19 (196...

Correspondence: [email protected] Department of Mathematics, Faculty of Science, Guelma University Guelma, Algeria Abstract In this article, sufficient conditions for the existence result of quasilinear multi-delay integro-differential equations of fractional orders with nonlocal impulsive conditions in Banach spaces have been presented using fractional calculus, resolvent operators, and ...

In this paper, we investigate the existence and uniqueness of solutions to boundary-value problems for second-order impulsive differential equations at resonance. To obtain these results, we apply fixed point methods and new differential inequalities.

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differe...

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Firstly, the surveys for studies on boundary value problems for higher order ordinary differential equations and for higher order fractional differential equations are given. Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented. Thirdly we propose four classes of higher order linear fractional differential eq...

* Correspondence: [email protected]. zj.cn School of Mathematical Sciences, Xiamen University, Xiamen, 361005, PR China Abstract In this article, a new nonlinear impulsive delay differential inequality is established, which can be applied in the dynamical analysis of nonlinear systems to improve many extant results. Using the inequality, we obtain some sufficient conditions to guarantee the exponen...

In this paper, by making use of the calculous technique and some results of the differential inequality, oscillatory properties of the solutions of certain impulsive delay hyperbolic partial differential equations with nonlinear diffusion term are investigated. A new sufficient criterion for oscillations of such equations is obtained.

Of concern is the existence of solutions to nonlocal impulsive Cauchy problems for evolution equations. Combining the techniques of operator semigroups, approximate solutions, noncompact measures and the fixed point theory, new existence theorems are obtained, which generalize and improve some previous results since neither the Lipschitz continuity nor compactness assumption on the impulsive fu...

Monotonicity of solutions is an important property in the investigation of oscillatory behaviors of differential equations. A number of papers provide some existence criteria for eventually positive increasing solutions. However, relatively little attention is paid to eventually positive solutions that are also eventually decreasing solutions. For this reason, we establish several new and sharp...