相关论文: Asymptotic solutions of forced nonlinear second or…
We consider the nonlinear Schr\"odinger equation $iu_t + \Delta u= \lambda |u|^{\frac {2} {N}} u $ in all dimensions $N\ge 1$, where $\lambda \in {\mathbb C}$ and $\Im \lambda \le 0$. We construct a class of initial values for which the…
The use of hyperasymptotics and the Weniger transformation has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals {evaluated across…
The almost sure rate of exponential-polynomial growth or decay of affine stochastic Volterra and affine stochastic finite-delay equations is investigated. These results are achieved under suitable smallness conditions on the intensities of…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…
We study integro-differential elliptic equations (of order $2s$) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this setting, both in divergence and non-divergence form.…
By revisiting an asymptotic integration theory of nonlinear ordinary differential equations due to J.K. Hale and N. Onuchic [Contributions Differential Equations 2 (1963), 61--75], we improve and generalize several recent results in the…
We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two key cases: cubic nonlinearities and higher-order power…
We present a new generalization of the steepest descent method introduced by Deift and Zhou for matrix Riemann-Hilbert problems and use it to study the semiclassical limit of the focusing nonlinear Schroedinger equation with real analytic,…
\noindent Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \begin{equation*} \Delta \left(r_{n}\left(\Delta \left(x_{n}+p_{n}x_{n-k}\right) \right)…
We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulation, whose novelty consists in including some asymptotically…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the signs of the parameters, we classify the difference…
In this paper we prove the well-posedness and we study the asymptotic behavior of nonoscillatory $L^p$-solutions for a third order nonlinear scalar differential equation. The equation consists of two parts: a linear third order with…
We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension…
In this manuscript, we derive Schauder estimates for viscosity solutions to non-convex fully nonlinear second-order parabolic equations \[ \partial_t u - F(x, t,D^2u) = f (x, t) \quad \text{in} \quad \mathrm{Q}_1 = B_1 \times (-1, 0], \]…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schr"odinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic…
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…