Second-order Impulsive Differential Inclusions Research Articles

An analysis concerning approximate controllability results for second-order Sobolev-type delay differential systems with impulses

This paper is devoted to studying the approximate controllability for second-order impulsive differential inclusions with infinite delay. For proving the main results, we use the results related to the cosine and sine function of operators, Martelli’s fixed point theorem, and the results when combined with the properties of differential inclusions. Firstly, we prove the approximate controllability for second-order impulsive differential inclusions with initial conditions. Then, we extend the discussion to the second-order impulsive system with nonlocal conditions. Finally, we provide an example for the illustration of the obtained theoretical results.

Infinitely Many Solutions for Second-Order Impulsive Differential Inclusions with Relativistic Operator

In this paper, the boundary value problem of second-order impulsive differential inclusion involving relativistic operator is studied. Infinitely many nonnegative solutions are obtained by using non-smooth critical point theorem for locally Lipschitz functionals.

Periodic solution for second-order impulsive differential inclusions with relativistic operator

In this paper, the boundary value problem of a second-order impulsive differential inclusion involving a relativistic operator is studied. First, the singular problem is reduced to an equivalent non-singular problem in order to better apply the variational methods. Then the existence of a periodic solution is obtained by nonsmooth critical point theory. Moreover, the boundedness and nonnegativity of solutions are obtained by restricting the discontinuous nonlinear term.

Impulsive differential inclusions via variational method

Abstract In this paper, we establish several results about the existence of second-order impulsive differential inclusion with periodic conditions. By using critical point theory, several new existence results are obtained. We also provide an example in order to illustrate the main abstract results of this paper.

Three solutions for second-order impulsive differential inclusions with Sturm-Liouville boundary conditions via nonsmooth critical point theory

A second-order impulsive differential inclusion with Sturm-Liouville boundary conditions is studied. By using a nonsmooth version of a three critical point theorem of Ricceri, the existence of three solutions is obtained.

Existence of solutions for second-order impulsive differential inclusions

In this paper, we investigate the existence and multiplicity of solutions to the following second-order impulsive Hamiltonian systems: where is a continuousmap form the interval [0, T] to the set of N-order symmetric matrices. Our methods are based on critical point theory for nondifferentiable functionals. Copyright © 2014 John Wiley & Sons, Ltd.

Existence and multiplicity of solutions for second-order impulsive differential inclusions

In this paper we consider a class of a second-order impulsive differential inclusions. Using a variational method based on the non-smooth critical point theory, we prove the existence and multiplicity of anti-periodic solutions.

Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters

Applying two three critical points theorems, we prove the existence of at least three anti-periodic solutions for a second-order impulsive differential inclusion with a perturbed nonlinearity and two parameters.

Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point theory

A nonsmooth version of a three critical point theorem of Ricceri (due to Iannizzotto) is used to obtain three anti-periodic solutions for a second-order impulsive differential inclusions with a perturbed nonlinearity and two parameters.