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Some results on stability and on characterization of K-convexity of set-valued functions

100%
Cardinali T., Papalini F.
Annales Polonici Mathematici
|
1993
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tom 58
|
nr 2
185-192
EN
We present a stability theorem of Ulam-Hyers type for K-convex set-valued functions, and prove that a set-valued function is K-convex if and only if it is K-midconvex and K-quasiconvex.
2
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Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

100%
Papageorgiou N. S., Papalini F.
Annales Polonici Mathematici
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2000
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tom 75
|
nr 2
125-141
EN
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
3

Convergence results for nonlinear evolution inclusions

100%
Cardinali T., Papalini F.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1995
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tom 15
|
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.
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