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Hyperbolic equations in uniform spaces

100%

Cholewa J. W. , Dlotko T.

tom Vol. 52, nr 3

249-263

The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of R^n. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space H[...]^R^n) x L[...](R^n). Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.

Remarks on some variants of minimal point theorem and Ekeland variational principle with applications

59%

Meghea I. , Stamin C. S.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

354--379

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.