On the Mazur-Orlicz theorem
On the Numerical Range in Reflexive Banach Spaces.
On the radius of a set in a Hilbert space
On the range of nonlinear operators with linear asymptotes which are not invertible
On the regularity of solutions in Convex Integration theory.
On the semigroup of mappings on Fréchet Montel space
On vector functions of bounded convexity
Let be a normed linear space. We investigate properties of vector functions of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity is equal to the variation of on . As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues
Soit un espace localement compact. Tout opérateur dissipatif de domaine dense dans est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur .À tout opérateur vérifiant le principe du maximum positif sur et de domaine assez riche, on associe un opérateur bilinéaire , appelé...
Optimization of Functions on Certain Subsets of Banach Spaces.
Periodic solutions to certain evolution inequalities
Porous medium equation and fast diffusion equation as gradient systems
We show that the Porous Medium Equation and the Fast Diffusion Equation, , with , can be modeled as a gradient system in the Hilbert space , and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions.
Practical Ulam-Hyers-Rassias stability for nonlinear equations
In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear equations...
Properties of the Preisach model for hysteresis.
Relative boundedness conditions and the perturbation of nonlinear operators
Remarks on Set-Contractions and Condensing Maps.
Remarks on subdifferentials of convex functionals
Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces
Some fixed point theorems for mappings satisfying Frum-Ketkov conditions
Some observations on local uniform boundedness principles. II
Some remarks on nonlinear functionals