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Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces

Jean-Marc Delort, Jérémie Szeftel (2005)

Journées Équations aux dérivées partielles

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.

Almost homoclinic solutions for a certain class of mixed type functional differential equations

Joanna Janczewska (2011)

Annales Polonici Mathematici

We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: q ̈ ( t ) + V q ( t , q ( t ) ) + u ( t , q ( t ) , q ( t - T ) , q ( t + T ) ) = f ( t ) , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....

Almost periodic and strongly stable semigroups of operators

Vũ Phóng (1997)

Banach Center Publications

This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators T n : n = 0 , 1 , . . . on a Banach space X (discrete one-parameter semigroups), one-parameter C 0 -semigroups T ( t ) : t ≥ 0 on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family of bounded...

Almost periodic generalized solutions of differential equations

Chikh Bouzar, Fethia Ouikene (2021)

Mathematica Bohemica

The paper aims to study systems of linear ordinary differential equations in the context of an algebra of almost periodic generalized ultradistributions. Conditions on the existence of generalized solutions are given.

Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays

Valéry Covachev, Zlatinka Covacheva, Haydar Akça, Eada Al-Zahrani (2003)

Open Mathematics

A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution....

Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)

Alexandr Fischer (1999)

Mathematica Bohemica

This paper generalizes earlier author's results where the linear and quasilinear equations with constant coefficients were treated. Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.

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