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Impulsive boundary value problems for p ( t ) -Laplacian’s via critical point theory

Marek Galewski, Donal O'Regan (2012)

Czechoslovak Mathematical Journal

In this paper we investigate the existence of solutions to impulsive problems with a p ( t ) -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Ait Dads, E., Benchohra, M., Hamani, S. (2009)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 34A37.In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered.

Impulsive periodic boundary value problem

Jan Draessler (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the paper we consider the impulsive periodic boundary value problem with a general linear left hand side. The results are based on the topological degree theorems for the corresponding operator equation ( I - F ) u = 0 on a certain set Ω that is established using properties of strict lower and upper functions of the boundary value problem.

Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

N.U. Ahmed (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.

Impulsive semilinear neutral functional differential inclusions with multivalued jumps

Nadjet Abada, Ravi P. Agarwal, Mouffak Benchohra, Hadda Hammouche (2011)

Applications of Mathematics

In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.

Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems

Song Zheng (2016)

Kybernetika

In this paper the issue of impulsive stabilization and synchronization of uncertain financial hyperchaotic systems with parameters perturbation is investigated. Applying the impulsive control theory, some less conservative and easily verified criteria for the stabilization and synchronization of financial hyperchaotic systems are derived. The control gains and impulsive intervals can be variable. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse...

Impulsive stabilization of high-order nonlinear retarded differential equations

Juan Liu, Xiaodi Li (2013)

Applications of Mathematics

In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods.

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