Lipschitzian superposition operators on metric semigroups and abstract convex cones of mappings of finite -variation.
Local Lipschitz continuity of the stop operator
On a closed convex set in with sufficiently smooth () boundary, the stop operator is locally Lipschitz continuous from into . The smoothness of the boundary is essential: A counterexample shows that -smoothness is not sufficient.
Local operators and a characterization of the Volterra operator.
Locally bounded spaces of vector functions and nonlinear operators therein.
Monotonic solutions for quadratic integral equations
Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
Multifunctions of two variables: examples and counterexamples
A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.
Multivalued superposition operators
Multi-valued superpositions [Book]
Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1 ... s ... n/p.
Nonlinear random operator equations and inequalities in Banach spaces.
Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis.
Nonlinear Spectral Theories and Solvability of Nonlinear Hammerstein Equations
AMS Subj. Classification: 47J10, 47H30, 47H10We study some possibilities of nonlinear spectral theories for solving nonlinear operator equations. The main aim is to research a spectrum and establish some kind of nonlinear Fredholm alternative for Hammerstein operator KF.
On a certain Volterra-Fredholm type integral equation.
On a characterization of the Preisach model for hysteresis
On a class of parabolic integro-differential equations.
On a nonlinear compactness lemma in .
On a sub-supersolution method for the prescribed mean curvature problem
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.
On a variational property of integral functionals and related conjectures
The aim of this paper is to give the proofs of those results that in [4] were only announced, and, at the same time, to propose some possible developments, indicating some of the most significant open problems.
On automatic boundedness of Nemytskiĭ set-valued operators
Let X, Y be two separable F-spaces. Let (Ω,Σ,μ) be a measure space with μ complete, non-atomic and σ-finite. Let be the Nemytskiĭ set-valued operator induced by a sup-measurable set-valued function . It is shown that if maps a modular space into subsets of a modular space , then is automatically modular bounded, i.e. for each set K ⊂ N(L(Ω,Σ,μ;X)) such that we have .
On characterization of the Lipschitzian composition operator between spaces of functions of bounded -variation