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Enclosures for the solution set of parametric interval linear systems

100%
Hladík M.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
561-574
EN
We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.
2
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On the solution set of a nonconvex nonclosed Sturm-Liouville type differential inclusion

100%
Cernea A.
Commentationes Mathematicae
|
2009
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tom 49
|
nr 2
EN
We consider a nonconvex and nonclosed Sturm-Liouville type differential inclusion and we prove the arcwise connectedness of the set of its solutions.
3

Convergence results for nonlinear evolution inclusions

88%
Cardinali T., Papalini F.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1995
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tom 15
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nr 1
43-60
EN
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 the multivalued perturbed problem x' ∈ -∂⁻f(x) + G(t,x), x(0) = x₀, where G:[0,T]×Ω → N(H) is a suitable multifunction.
4
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An existence result for impulsive functional differential inclusions in Banach spaces

75%
Benedetti I.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2004
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tom 24
|
nr 1
13-30
EN
We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.
5

Existence and density results for retarded subdifferential evolution inclusions

63%
Cardinali T., Pieri S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
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tom 16
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nr 1
53-74
EN
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 theorem"). Then we prove that this density result allows one to establish a nonlinear "bang-bang principle" for a class of control systems with dealy on a nonconvex constraint. We want to observe that the results here extend those of [11] and [13].
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