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Remarks on damped Schrodinger equation of Choquard type

Chergui Lassaad

Opuscula Mathematica

2021

Vol. 41, no. 4

465--488

This paper is devoted to the Schrodinger-Choquard equation with linear damping. Global existence and scattering are proved depending on the size of the damping coefficient.

Abstract Interpretations in the Framework of Invariant Sets

Alexandru A., Ciobanu G.

Fundamenta Informaticae

2016

Vol. 144, nr 1

1--22

We present a theory of abstract interpretations in the framework of invariant sets by translating the notions of lattices and Galois connections into this framework, and presenting their properties in terms of finitely supported objects. We introduce the notions of invariant correctness relation and invariant representation function, emphasize an equivalence between them, and establish the relationship between these notions and invariant Galois connections. Finally, we provide some widening and narrowing techniques in order to approximate the least fixed points of finitely supported transition functions.

Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems

Barakova L.

Demonstratio Mathematica

2001

Vol. 34, nr 3

559-576

In this paper a 2-dimensional real autonomous system with polynomial right-hand sides of a concrete type is studied. Hopf bifurcation is analysed and existence of a limit cycle is proved. A new formula to determine stability or unstability of this limit cycle is introduced. A positively invariant set, which is globally attractive, is found. Consequently, existence of a stable limit cycle around an unstable critical point is proved and also a sufficient condition for non-existence of a closed trajectory in the phase space is given. Global characteristics of the system are studied. An application in economics to the dynamic version of the neo-keynesian macroeconomic IS-LM model is presented.