Related papers: Almost periodic solutions of periodic linear parti…
The paper is dedicated to studying the problem of Poisson stability (in particular stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in the sense of…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
We are concerned with some extensions of the classical Liouville theorem for bounded harmonic functions to solutions of more general equations. We deal with entire solutions of periodic and almost periodic parabolic equations including the…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
We prove a necessary and sufficient condition for the existence of a $T$-periodic solution for the time-periodic second order differential equation $\ddot{x}+f(t,x)+p(t,x,\dot x)=0$, where $f$ grows superlinearly in $x$ uniformly in time,…
A continuous solution of an algebraic equation with holomorphic almost periodic coefficients is also almost periodic.
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…
This paper deals with the existence of asymptotic almost automorphic solution of fractional integro differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study…
We prove the existence of at least one T-periodic solution (T > 0) for differential equations of the form (u'(t)/sqrt{1-u'^2(t)})'=f(u(t))+h(t), in (0,T), where f is a continuous function defined on R that satisfies a strong resonance…
We are concerned with periodic problems for nonlinear evolution equations at resonance of the form $\dot u(t) = - A u(t) + F (t,u(t))$, where a densely defined linear operator $A\colon D(A)\to X$ on a Banach space $X$ is such that $-A$…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…
In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the…
We discuss the notion of resonance, as well as the existence and uniqueness of periodic solutions for a forced simple harmonic oscillator. While this topic is elementary, and well-studied for sinusoidal forcing, this does not seem to be the…