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Eventually positive solutions for nonlinear impulsive differential equations with delays

Shao Yuan Huang, Sui Sun Cheng (2012)

Annales Polonici Mathematici

Several recent oscillation criteria are obtained for nonlinear delay impulsive differential equations by relating them to linear delay impulsive differential equations or inequalities, and then comparison and oscillation criteria for the latter are applied. However, not all nonlinear delay impulsive differential equations can be directly related to linear delay impulsive differential equations or inequalities. Moreover, standard oscillation criteria for linear equations cannot be applied directly...

Existence and controllability of fractional-order impulsive stochastic system with infinite delay

Toufik Guendouzi (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic infinite delay integro-differential equations in Hilbert space. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided...

Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses

Changjin Xu, Qianhong Zhang, Maoxin Liao (2013)

Applications of Mathematics

In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.

Existence and positivity of solutions for a nonlinear periodic differential equation

Ernest Yankson (2012)

Archivum Mathematicum

We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.

Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces

Zuomao Yan, Hongwu Zhang (2014)

Annales Polonici Mathematici

We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the α-resolvent operator. An example is given to illustrate the...

Existence results for impulsive fractional differential equations with p -Laplacian via variational methods

John R. Graef, Shapour Heidarkhani, Lingju Kong, Shahin Moradi (2022)

Mathematica Bohemica

This paper presents several sufficient conditions for the existence of at least one classical solution to impulsive fractional differential equations with a p -Laplacian and Dirichlet boundary conditions. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.

Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

Hammouche Hadda, Guerbati Kaddour, Benchohra Mouffak, Abada Nadjat (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.

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