Semilinear Differential Inclusions Research Articles

Viability for quasi-autonomous semilinear evolution inclusions

We provide some invariance properties for a closed graph with respect to quasi-autonomous semilinear differential inclusion. As applications, we study a Lipshitz regularity of the solution set and we give a relaxation result. Furthermore, we get null controllability results for semilinear control systems.

Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces

In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Existence of Infinitely Many Periodic Solutions for Perturbed Semilinear Fourth-Order Impulsive Differential Inclusions

This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals.

Nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces

In this paper we present two existence results of nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces. The first result relies on a growth condition on the whole time interval. Our second result relies on a revised growth condition which is divided into two parts, one for the subintervals containing the points associated with the nonlocal conditions, and the other for the rest of the interval. The used technique is based on fractional calculus, the properties of the measure of noncompactness and a powerful fixed point theorem for multifunctions due to O’Regan–Precup. Finally, we apply the theoretical results to fractional differential inclusions on lattices with global neighborhood interactions.

Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions

Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions

О нелокальных граничных задачах для полулинейных дифференциальных включений

О нелокальных граничных задачах для полулинейных дифференциальных включений

Задача управляемости для импульсных полулинейных вырожденных функционально-дифференциальных включений с бесконечным запаздыванием

Задача управляемости для импульсных полулинейных вырожденных функционально-дифференциальных включений с бесконечным запаздыванием

Existence and Controllability Results for Fractional Stochastic Semilinear Differential Inclusions

In this paper, we prove the existence and controllability results for fractional stochastic semilinear differential inclusions involving the Caputo derivative in Hilbert spaces. The results are obtained by using fractional calculation, operator semigroups and Bohnenblust-Karlin fixed point theorem. An example is provided to illustrate the theory.

Controllability for systems governed by semilinear evolution inclusions without compactness

In this paper we study the controllability for a class of semilinear differential inclusions in Banach spaces. Since we assume the regularity of the nonlinear part with respect to the weak topology, we do not require the compactness of the evolution operator generated by the linear part. As well we are not posing any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. We are considering the usual assumption on the controllability of the associated linear problem. Notice that, in infinite dimensional spaces, the above mentioned compactness of the evolution operator and linear controllability condition are in contradiction with each other. We suppose that the nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. This regularity setting allows us to solve controllability problem under various growth conditions. As application, a controllability result for hyperbolic integro-differential equations and inclusions is obtained. In particular, we consider controllability of a system arising in a model of nonlocal spatial population dispersal and a system governed by the second order one-dimensional telegraph equation.

Periodic Solutions for Semilinear Fourth-Order Differential Inclusions via Nonsmooth Critical Point Theory

Three periodic solutions with prescribed wavelength for a class of semilinear fourth-order differential inclusions are obtained by using a nonsmooth version critical point theorem. Some results of previous related literature are extended.

Near viability for fully nonlinear differential inclusions

AbstractWe consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

Existence results for abstract semilinear evolution differential inclusions with nonlocal conditions

In this paper, we use a new method to study semilinear evolution differential inclusions with nonlocal conditions in Banach spaces. We derive conditions for F and g for the existence of mild solutions. The results obtained here improve and generalize many known results.

On controllability for nonconvex semilinear differential inclusions

On controllability for nonconvex semilinear differential inclusions

Necessary and sufficient conditions for approximate strong invariance for semilinear differential inclusions

We establish necessary and sufficient conditions for approximate strong invariance referring to semilinear differential inclusions, conditions expressed in terms of a suitable defined tangency concept.

Implementing Galerkin Finite Element Methods for Semilinear Elliptic Differential Inclusions

Abstract. This paper presents the first feasible method for the approximation of solution sets of semi-linear elliptic partial differential inclusions. It is based on a new Galerkin Finite Element approach that projects the original differential inclusion to a finite-dimensional subspace of . The problem that remains is to discretize the unknown solution set of the resulting finite-dimensional algebraic inclusion in such a way that efficient algorithms for its computation can be designed and error estimates can be proved. One such discretization and the corresponding basic algorithm are presented along with several enhancements, and the algorithm is applied to two model problems.

Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

We firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions. Secondly, we establish two cases of sufficient conditions for the controllability of the considered control problems.

Mild Solutions for Nonlocal Impulsive Fractional Semilinear Differential Inclusions with Delay in Banach Spaces

In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We consider the case when the values of the orient field are convex as well as nonconvex. Our obtained results improve and generalize many results proved in recent papers.

Existence results for fractional semilinear differential inclusions in Banach spaces

We consider the existence of mild solutions for fractional semilinear differential inclusions involving a nonconvex set-valued map in Banach spaces. First, we study the continuous property of the solution map for an auxiliary fractional differential equation. Then the main result is obtained by using this solution map, selection theorems from multivalued analysis and Schauder’s fixed point theorem. Finally an example to illustrate the applications of the main result is also given.

Impulsive semilinear evolution differential inclusions with nonconvex right hand side

In this paper we prove the existence of a mild solution for a impulsive semilinear evolution differential inclusions with infinite delay in a separable Banach space.

Existence of solutions for a class of boundary value problems of semilinear differential inclusions

In this paper, a class of boundary problems for second order semilinear differential inclusions is studied. By applying techniques from multivalued analysis and fixed point theorems due to Covitz–Nadler, Bohnenblust–Karlin and Schaefer, some existence results of solutions are presented for the nonlinear term which is a Lipschitz continuous, upper or lower semicontinuous multivalued map, respectively. As consequences some existence conditions of solutions are given for a class of second order semilinear differential systems.