Second-order Differential Inclusions Research Articles

On Monotone Solutions for a Nonconvex Second-Order Differential Inclusion with Memory

Abstract The existence of monotone solutions for a second-order differential inclusion with memory is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Clarke subdifferential of a uniformly regular function.

Singular-perturbation method for nonlinear second-order evolution inclusions with Volterra operators

We consider a class of second-order operator differential inclusions with Volterra-type operators. Using the singular-perturbation method, we study the problem of the existence of a solution of the Cauchy problem for these inclusions. Important a priori estimates are obtained for solutions and their derivatives. We give an example that illustrates the proposed approach to the analysis of the problem under consideration.

Remarks on the Existence Results for Second-Order Differential Inclusions with Nonlocal Conditions

In this paper, we investigate the existence of mild solutions of second-order initial-values problems for a class of semilinear differential inclusions with nonlocal conditions. By using suitable fixed-point theorems for multi-valued maps, we study the case where the multi-valued map F has convex or nonconvex values.

Bound sets approach to boundary value problems for vector second-order differential inclusions

A continuation principle is established for the solvability of vector second-order boundary value problems associated with upper-Carathéodory differential inclusions. For Floquet second-order problems, this principle is combined with a bound sets approach. The viability result is also obtained in this way.

On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases.

Three-dimensional optimal deployment of a tethered subsatellite with an elastic tether

This paper presents the nonlinear optimal control for the deployment process of an elastically tethered subsatellite model, which involves not only the usually addressed in-plane motion, but also the out-of-plane motion. All the nonlinearities in the system model and the mission-related state-control constraints are taken into consideration. Instead of the commonly used state-space model, a second-order differential inclusion formulation is exploited in this paper to achieve a significant reduction of the number of system variables. The optimal control is solved by discretizing the optimal control problem first and then solving the resulting large-scale optimization problem. The case studies in the paper demonstrate well the performance of the proposed strategy.

A selection of oscillation criteria for second-order differential inclusions

Oscillation criteria are presented for second-order differential inclusions ( a ( t ) y ′ ( t ) ) ′ ∈ F ( t , y ( t ) ) for a.e. t ≥ t 0 ≥ 0 . We note that the results of this paper are new even in the single valued case.

Nonconvex-valued impulsive functional differential inclusions with variable times

We use the Schaefer fixed-point theorem, combined with the Bressan-Colombo selection theorem for lower-semicontinuous multivalued operators with nonempty closed and decomposable values, for the investigation of the existence of solutions for first-and second-order impulsive functional differential inclusions with variable times.

Existence solutions for second-order differential inclusions with nonconvex perturbations

The article studies the three-point boundary value problems for second-order perturbed differential inclusions of the form a.e. on [0,1]. The existence of solutions is proved under nonconvexity condition for the multifunction H.

Solvability of Langevin differential inclusions with set-valued diffusion terms on Riemannian manifolds

The existence of weak solution is proved for a Langevin type second-order stochastic differential inclusion on a complete Riemannian manifold, having both drift and diffusion terms set-valued. The construction of solution involves integral operators with Riemannian parallel translation and a special sequence of continuous ϵ-approximations for an upper semicontinuous set-valued mapping with convex bounded closed values, that is proved to converge point-wise to a Borel measurable selection.

Subharmonic solutions for nonautonomous sublinear second-order differential inclusions systems with [formula omitted]-Laplacian

An existence result is obtained for infinite subharmonic solutions of nonautonomous second-order sublinear differential inclusions systems with p -Laplacian by the minimax methods in the critical point theory.

Existence and Controllability Results for First-and Second-Order Functional Semilinear Differential Inclusions with Nonlocal Conditions

In this paper, we prove existence and controllability results for first- and second-order semilinear differential inclusions in Banach spaces with nonlocal conditions.

Controllability of Second-Order Differential and Integro-Differential Inclusions in Banach Spaces

In this paper, the controllability of second-order differential and integro-differential inclusions in Banach spaces are investigated. Two new results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multivalued maps.

Existence results for second-order impulsive functional differential inclusions

The existence of solutions on a compact interval to second-order impulsive functional differential inclusions is investigated. Several new results are obtained by using Sadovskii's fixed point theorem.

Upper and lower solutions method for differential inclusions with integral boundary conditions

A nonlinear alternative of the Leray-Schauder type for multivalued maps combined with upper and lower solutions is used to investigate the existence of solutions for second-order differential inclusions with integral boundary conditions.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

On the two‐point boundary value problem for quadratic second‐order differential equations andinclusions on manifolds

The two‐point boundary value problem for second‐order differential inclusions of the form (D/dt)ṁ(t) ∈ F(t, m(t), ṁ(t)) on complete Riemannian manifolds is investigated for a couple of points, nonconjugate along at least one geodesic of Levi‐Civitá connection, where D/dt is the covariant derivative of Levi‐Civitá connection and F(t, m, X) is a set‐valued vector with quadratic or less than quadratic growth in the third argument. Some interrelations between certain geometric characteristics, the distance between points, and the norm of right‐hand side are found that guarantee solvability of the above problem for F with quadratic growth in X. It is shown that this interrelation holds for all inclusions with F having less than quadratic growth in X, and so for them the problem is solvable.

CONTINUOUS DEPENDENCE ON DATA FOR VIBRO-IMPACT PROBLEMS

We consider vibro-impact problems, i.e. mechanical systems with a finite number of degrees of freedom subject to frictionless unilateral constraints. The dynamics is described by a second-order measure differential inclusion completed by an impact law of Newton's type. Motivated by the computation of approximate solutions, we study in this paper the continuous dependence of solutions on data. When several constraints can be active at the same time, continuity on data does not hold in general and an example of such a behavior is presented. We then propose a criterion involving the geometry of the active constraints along the limit trajectory which ensures continuity on data.

Existence Results on the Second-Order Nonconvex Sweeping Processes with Perturbations

We prove several existence theorems for second-order differential inclusions of the form $$\dot x(t) \in K(x(t)),\ddot x(t) \in - N(K(x(t));\dot x(t)) + F(t,x(t),\dot x(t))$$ , when K and F are two convex or nonconvex set-valued mappings taking their values in a Hilbert space.

Nonresonance impulsive functional differential inclusions with variable times

In this paper, we investigate the existence of solutions for first- and second-order nonresonance impulsive functional differential inclusions with variable moments. The proofs make use of the Martelli fixed-point theorem for condensing multivalued maps.