Existence results for second-order neutral functional differential and integrodifferential inclusions in Banach spaces.
Existence results of nonconvex differential inclusions.
Fixed time impulsive differential inclusions.
Flow invariance for perturbed nonlinear evolution equations.
General existence results for nonconvex third order differential inclusions.
General existence results for second order nonconvex sweeping process with unbounded perturbations.
Gradient flows of non convex functionals in Hilbert spaces and applications
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Identification problems for degenerate parabolic equations
This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different...
Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions
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
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.
Minty variational inequalities and monotone trajectories of differential inclusions.
Mixed type semicontinuous differential inclusions in Banach spaces
We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.
Multivalued linear operators and differential inclusions in Banach spaces
In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued...
Multivalued semilinear neutral functional differential equations with nonconvex-valued right-hand side.
Near viability for fully nonlinear differential inclusions
We 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...
Neumann boundary-value problems for differential inclusions in Banach spaces.
Neutral functional differential and integrodifferential inclusions in Banach spaces
In questo lavoro studiamo l'esistenza di soluzioni deboli su un intervallo compatto di problemi con valore iniziale per inclusioni funzionali neutre differenziali e integrodifferenziali in spazi di Banach. I risultati sono ottenuti usando un teorema di punto fisso per mappe condensanti dovuto a Martelli.
Non-degenerate implicit evolution inclusions.
Nonlinear evolution inclusions arising from phase change models
The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.
Nonlinear variational evolution inequalities in Hilbert spaces.