Differential equations in metric spaces
Differential inclusions and multivalued integrals
In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented...
Discretization methods for nonconvex differential inclusions.
Euler approximation of nonconvex discontinuous differential inclusions.
Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms
Similarly to quasidifferential equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. In spite of lacking any linear structures, a distribution-like approach leads to so-called right-hand forward solutions. These extensions are mainly motivated by compact subsets of the Euclidean space...
Evolution inclusions in non separable Banach spaces
We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.
Existence and approximation results for gradient flows
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure...
Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions.
Existence of mild solutions of a semilinear nonconvex differential inclusion with nonlocal conditions
Existence of mild solutions of second order initial value problems for delay integrodifferential inclusions with nonlocal conditions
In this paper we investigate the existence of mild solutions to second order initial value problems for a class of delay integrodifferential inclusions with nonlocal conditions. We rely on a fixed point theorem for condensing maps due to Martelli.
Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces
In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
Existence of mild solutions to semilinear evolution inclusions with nonlocal conditions.
Existence of solutions for differential inclusions on closed moving constraints in Banach spaces.
Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space.
Existence of solutions for second order stochastic differential inclusions in Hilbert spaces
In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.
Existence of viable solutions for nonconvex differential inclusions.
Existence results for first order impulsive semilinear evolution inclusions.
Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces.
Existence results for second-order neutral functional differential and integrodifferential inclusions in Banach spaces.