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An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces

M. Poppenberg (1999)

Studia Mathematica

A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces C ∞ ( K ) , S ( ℝ N ) , B ( ℝ R N ) , D L 1 ( ℝ N ) , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

An averaging principle for stochastic evolution equations. II.

Bohdan Maslowski, Jan Seidler, Ivo Vrkoč (1991)

Mathematica Bohemica

In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.

An existence result for impulsive functional differential inclusions in Banach spaces

Irene Benedetti (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.

An interplay between the weak form of Peano's theorem and structural aspects of Banach spaces

C. S. Barroso, M. A. M. Marrocos, M. P. Rebouças (2013)

Studia Mathematica

We establish some results that concern the Cauchy-Peano problem in Banach spaces. We first prove that a Banach space contains a nontrivial separable quotient iff its dual admits a weak*-transfinite Schauder frame. We then use this to recover some previous results on quotient spaces. In particular, by applying a recent result of Hájek-Johanis, we find a new perspective for proving the failure of the weak form of Peano's theorem in general Banach spaces. Next, we study a kind of algebraic genericity...

Anti-periodic solutions to a parabolic hemivariational inequality

Jong Yeoul Park, Hyun Min Kim, Sun Hye Park (2004)

Kybernetika

In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form b ( u ) , where b ∈ L loc ∞ ( R ) . Extending b to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

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