Displaying similar documents to “On a time-dependent subdifferential evolution inclusion with Carathéodory perturbation”

A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

Similarity:

A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.

Existence and relaxation results for nonlinear second order evolution inclusions

Stanisław Migórski (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.

Convergence results for nonlinear evolution inclusions

Tiziana Cardinali, Francesca Papalini (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for...

On the Conley index in Hilbert spaces - a multivalued case

Zdzisław Dzedzej (2007)

Banach Center Publications

Similarity:

We introduce the cohomological Conley type index theory for multivalued flows generated by vector fields which are compact and convex-valued perturbations of some linear operators.

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

Similarity:

Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

Mouffak Benchohra (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

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 and density results for retarded subdifferential evolution inclusions

Tiziana Cardinali, Simona Pieri (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation...