Related papers: Solutions of algebraic equations with analytic alm…
Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and…
Whenever all differences between zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
In an abstract Banach space we study conditions for the existence of piecewise continuous, almost periodic solutions for semi-linear impulsive differential equation with fixed and non-fixed moments of impulsive action
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies the almost…
Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components…
We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length…
In this paper, we first use the Bohr property to give a definition of Besicovitch almost periodic functions, and study some basic properties of Besicovitch almost periodic functions, including the equivalence of the Bohr property and the…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…
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.
We prove, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of…
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…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
We compute fundamental solutions of homogeneous elliptic differential operators, with constant coefficients, on $\mathbb{R}^n$ by mean of analytic continuation of distributions. The result obtained is valid in any dimension, for any degree…
By the extension of the 3-dimensional analytical solutions of Goldreich and Weber "P. Goldreich and S. Weber, Homologously Collapsing Stellar Cores, Astrophys, J. 238, 991 (1980)" with adiabatic exponent gamma=4/3, to the (classical)…