Related papers: Justification of an asymptotic expansion at infini…

The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…

In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…

This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…

In this paper we consider the initial value problem for a family of shallow water equations on the line $\R$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as…

We study the precise asymptotic behavior of a non-trivial solution that converges to zero, as time tends to infinity, of dissipative systems of nonlinear ordinary differential equations. The nonlinear term of the equations may not possess a…

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…

Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

We give an asymptotic equivalent at infinity of the unbounded solutions of some boundary layer equations arising in fluid mechanics.

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…

We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high order of approximation.

We prove that there exists an entire function for which every complex number is an asymptotic value and whose growth is arbitrarily slow subject only to the necessary condition that the function is of infinite order.

In this paper, we show how solutions to explicit algebraic systems lead to solutions to infinite families of modular differential equations.

Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…

This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time…

The asymptotic study of a time-dependent function $f$ as the solution of a differential equation often leads to the question of whether its derivative $\dot f$ vanishes at infinity. We show that a necessary and sufficient condition for this…

In this paper, we prove the existence of asymptotic speed of solutions to fully nonlinear, possibly degenerate parabolic partial differential equations in a general setting. We then give some explicit examples of equations in this setting…

We obtain a quantitative high order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine the study of the asymptotic behavior of the Monge-Amp\`ere equation, the special Lagrangian…

We will prove an infinite family of asymptotic formulas for the logarithm of certain two-colored partitions. An infinite sub-family of these asymptotics was posed as a conjecture by Guadalupe.