相关论文: Existence of Doubly-Weighted Pseudo Almost Periodi…
The almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr's fundamental…
We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…
We study conditions for the abstract linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t), t\ge 0$ to have asymptotic almost periodic solutions, where $F(\cdot )$ is periodic, $f$ is asymptotic almost periodic. The main…
We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$ where $A, B$ are densely defined closed linear operators acting in a…
In this paper, we prove existence of \emph{very weak solutions} to nonhomogeneous quasilinear parabolic equations beyond the duality pairing. The main ingredients are a priori esitmates in suitable weighted spaces combined with the…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the…
We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only…
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…
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…
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 simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has…
In this paper we investigate existence and characterization of non-radial pseudo-radial (or separable) solutions of some semi-linear elliptic equations on symmetric 2-dimensional domains. The problem reduces to the phase plane analysis of a…
The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…
We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be expressed as diagonal system with a perturbation which is small enough. Moreover we show that the diagonal terms are contained in…
In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone…
In this paper, we first propose a new concept of almost periodic time scales, a new definition of almost automorphic functions on almost periodic time scales, and study some their basic properties. Then we prove a result ensuring the…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…