相关论文: Periodic solutions of semi-explicit differential-a…

Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…

The existence of a semiconjugate relation permits the transformation of a higher order difference equation on a group into an equivalent triangular system of two difference equations of lower orders. Introducing time-dependent form…

We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…

In this paper we study the conditions, under which the quaternionic Riccati equations have periodic solutions. The obtained result we compare with one recently obtained important one.

A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…

We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…

Time-periodic form or expression is a ubiquitous natural and man-made phenomenon observable in all the scientific and engineering disciplines. In this article, we propose a theory of periodic sequence (TPS), which can be formulated as a…

We study a semilinear elliptic equation with a pure power nonlinearity with exponent $p>1$, and provide sufficient conditions for the existence of positive solutions. These conditions involve expected exit times from the domain, $D$, where…

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And…

This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…

We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…

We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…

We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This generalizes…

This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…

In this study, we investigate a mixed problem linked to a second-order parabolic equation, characterized by temporal dependencies and variable~coefficients, and constrained by non-local, non-self-adjoint boundary conditions. By defining…

This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an $n$-dimensional ball. By combining the variational methods and saddle point reduction technique, we prove there exist at least…