Characterization of globally Lipschitzian composition operators in the Banach space
We give a characterization of the globally Lipschitzian composition operators acting in the space
Common fixed points of biased maps of type and applications.
Commutators in real interpolation with quasi-power parameters.
Compactness and existence results for ordinary differential equations in Banach spaces.
Composing infinitely differentiable functions.
Continuity and Fréchet-Differentiability of Nemytskij Operators in Hölder Spaces.
Continuity of hysteresis operators in Sobolev spaces
We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces for , (localy) Lipschitz continuous in and discontinuous in for arbitrary . Examples show that this result is optimal.
Continuity of superposition operators on and
Continuity of the superposition of set-valued functions.
Convex solutions of a nonlinear integral equation of Urysohn type.
Differential inequalities for hysteresis systems.
Dividing measures and narrow operators
We use a new technique of measures on Boolean algebras to investigate narrow operators on vector lattices. First we prove that, under mild assumptions, every finite rank operator is strictly narrow (before it was known that such operators are narrow). Then we show that every order continuous operator from an atomless vector lattice to a purely atomic one is order narrow. This explains in what sense the vector lattice structure of an atomless vector lattice given by an unconditional basis is far...
Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting
In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions Δ₂ and...
Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting
In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type...
Equations with discontinuous nonlinear semimonotone operators
The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type with the discontinuous semimonotone operator . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in are given for illustration.
Exact controllability of generalized Hammerstein type integral equation and applications.
Existence and multiplicity results for nonlinear noncoercive equations
Existence of solutions for some Hammerstein type integro-differential inclusions.
Existence of solutions of a functional-integral equation in infinite dimensional Banach spaces
Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps.