Results 241 to 250 of about 773 (267)

The discrete Painlevé I equations: transcendental integrability and asymptotic solutions

Journal of Physics A: Mathematical and General, 2001
Summary: The integrability of the discrete Painlevé I equation (dP-I) is reviewed and its integrability studied. We establish the existence of a conserved quantity which is algebraic in the case of the autonomous dP-I equation and it is argued that the non-autonomous dP-I map has a non-algebraic invariant. Our analysis leads to, among other results the
Bernardo, M., Truong, T. T., Rollet, G.
openaire   +1 more source

Bell Polynomials in the Mathematica System and Asymptotic Solutions of Integral Equations

Theoretical and Mathematical Physics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marichev, O. I., Slavyanov, S. Yu., Brychkov, Yu. A.   +2 more
openaire   +1 more source

UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS

Journal of Computational Acoustics, 2001
Uniformly asymptotic frequency-domain solutions for a class of hyperbolic equations with singular convolution operators are derived. Asymptotic solutions for this class of equations involve additional parameters — called attenuation parameters — which control the smoothing of the wavefield at the wavefront.
Hanyga, A., Seredyńska, M.
openaire   +1 more source

Exact, approximate and asymptotic solutions of the Klein–Gordon integral equation

Journal of Engineering Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fabrikant, V. I., Karapetian, E., Kalinin, S. V.   +2 more
openaire   +2 more sources

Asymptotic expansion of the solutions of integral equations with δ-form kernels

USSR Computational Mathematics and Mathematical Physics, 1972
Abstract WE consider the problem of constructing asymptotic expansions of the solutions of integral equations of the second kind depending on a small parameter ϵ 〉 0 in such a way that as ϵ 〉 0 the kernel of the integral operator has the nature of a δ-function.
openaire   +1 more source

On the asymptotic behaviour of solutions of nonlinear integral equations in BANACH spaces

Mathematische Nachrichten, 1979
AbstractThe asymptotic behaviour of solutions of nonlinear VOLTERRA integral equations is studied in a real BANACH spaces. The nonlinear operator is assumed to satisfy some accretivity‐type conditions.
openaire   +1 more source

ASYMPTOTIC BEHAVIOR OF THE SOLUTION OF A SINGULAR INTEGRAL EQUATION WITH A SMALL PARAMETER

Mathematics of the USSR-Sbornik, 1976
We construct an asymptotic expansion as that is uniform in of the solution of the singular integral equation Bibliography: 3 titles.
openaire   +1 more source

On the Asymptotic Behavior of Finite Energy Solutions of an Abstract Integral Equation

SIAM Journal on Mathematical Analysis, 1978
We define an energy function for a solution of the abstract nonlinear integral equation \[x'(t) + \partial \varphi (x(t)) + \int_0^t {a(t - s)\partial \psi (x(s))ds \ni f(t)} \quad (t \in R^ + ),\] and study the asymptotic behavior of the solutions for which the energy function is bounded. We also investigate the problem of getting an a priori bound on
openaire   +1 more source

Asymptotic Integration of the Principal Solution of a Second-Order Differential Equation

Bulletin of the London Mathematical Society, 1991
The second-order linear differential equation \((r(t)x')'+(f(t)+q(t))x=0\) is considered as a perturbation of the equation \((r(t)y')'+f(t)y=0\), where \(r,f,q,x\) and \(y\) are continuous real-valued and \(r>0\). It is known that if the unperturbed equation is nonoscillatory it has a unique principal solution \(y_ 1\) (up to a constant factor) such ...
openaire   +1 more source

Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity

Mathematics, 2022
A A Kashchenko
exaly