Heteroclinic connections for a class of non-autonomous systems.
A note on nontrivial periodic solutions of dynamical systems with subquadratic potential.
We obtain non-constant periodic solutions for a class of second-order autonomous dynamic systems whose potential is subquadratic at infinity. We give a theorem on conjugate points for convex potentials.
Heteroclinics for a class of fourth order conservative differential equations
Characterization of Globally Lipschitz Nemytskiĭ Operators Between Spaces of Set-Valued Functions of Bounded φ-Variation in the Sense of Riesz
Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC(Y) be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ operators, i.e. the composition operators defined by (Nu)(t) = H(t,u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space into (both are spaces of functions of bounded φ-variation in the sense of Riesz), and if it is globally Lipschitz, then it has to be of the form H(t,u(t)) = A(t)u(t)...
Topologías fuertes en espacios linealmente topologizados de funciones continuas.
Some remarks on the algebra of functions of two variables with bounded total -variation in Schramm sense
This paper is devoted to discuss some generalizations of the bounded total -variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total -variation in Schramm sense has the structure of a Banach algebra.
On a result of Adasch and Ernst.
Embedding in
If is a measurable space and a Banach space, we provide sufficient conditions on and in order to guarantee that , the Banach space of all -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of if and only if does.
Pták homomorphism theorem revisited
Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.
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