Related papers: Solutions of algebraic equations with analytic alm…
We consider 1D completely resonant nonlinear wave equations of the type v_{tt}-v_{xx}=-v^3+O(v^4) with spatial periodic boundary conditions. We prove the existence of a new type of quasi-periodic small amplitude solutions with two…
A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence,which corresponds periodic solutions in distribution for stochastic differential equations. On the basis of technique of upper and lower solutions and…
This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…
This work deals with almost automorphy of distributions. We give characterizations and main properties of these distributions. We also study the existence of distributional almost automorphic solutions of linear difference-differential…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
We solve Abreu's equation with periodic right hand side, in any dimension. This can be interpreted as prescribing the scalar curvature of a torus invariant metric on an Abelian variety.
Analytical periodic solutions for weakly Coupled Map Lattices are shown in an explicit form as well as in a recurrence relation. The results establish a link between a matricial representation and recurrence relations of the solutions.
We study hyperbolized versions of cohomological equations that appear with cocycles by isometries of the euclidean space. These (hyperbolized versions of) equations have a unique continuous solution. We concentrate in to know whether or not…
We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
This is a short review of the construction of quasi-periodic (algebraic-geometrical) solutions to hierarchies of nonlinear integrable equations. As is well known, the solutions are expressed through Riemann's theta-functions associated with…
By a classical result, solutions of analytic elliptic PDEs, like the Laplace equation, are analytic. In many instances, the properties that come from being analytic are more important than analyticity itself. Many important equations are…
In this paper, we prove some invariant curve theorems for the planar almost periodic reversible mappings. As an application, we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the nonlinear…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.
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 discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…
Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational,…