Results 21 to 30 of about 47,739 (313)

Regularized asymptotics of solutions to integro-differential partial differential equations with rapidly varying kernels

Ufa Mathematical Journal, 2018
. We generalize the Lomov’s regularization method for partial differential equations with integral operators, whose kernel contains a rapidly varying exponential factor.
A. Bobodzhanov, V. F. Safonov
semanticscholar   +1 more source

Asymptotics of the Solutions to Singularly Perturbed Integral Equations

Journal of Mathematical Analysis and Applications, 1993
The authors study the asymptotics of \(h_ \varepsilon\) as \(\varepsilon \to 0\), where \(h_ \varepsilon\) is a solution of the integral equation \((*)\) \(\varepsilon h_ \varepsilon+Rh_ \varepsilon=f\), \(\varepsilon>0\), \(Rh_ \varepsilon(x)=\int^ \beta_ \alpha R(x-y)h_ \varepsilon(y)dy\) with \(R(x)=P(D)G(x)\), \(P(D)=\sum^ p_{j=0}a_ jD^ j\), \(D=d ...
Ramm, A.G., Shifrin, E.I.
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Regularity Properties, Representation of Solutions, and Spectral Asymptotics of Systems with Multiplicities [PDF]

, 2004
Properties of solutions of generic hyperbolic systems with multiple characteristics with microlocally diagonalizable principal part are investigated.
I. Kamotski, Michael Ruzhansky
semanticscholar   +1 more source

Asymptotic behavior of solutions to functional integral equation with deviating arguments

Electronic Journal of Differential Equations, 2008
Summary: This article presents results on the existence and asymptotic behavior of solutions of a functional integral equation with deviating arguments. The proof of our main result uses the classical Schauder fixed point theorem and the technique of measures of noncompactness.
K. Balachandran, M. Diana Julie
openalex   +3 more sources

Asymptotics of the Solutions to Singularly Perturbed Multidimensional Integral Equations

Journal of Mathematical Analysis and Applications, 1995
The object of the study in the paper is the singularly perturbed integral equation of the form \[ \varepsilon h_ \varepsilon(x)+ \int_ T R(x- y) h_ \varepsilon(y) dy= f(x),\tag{1} \] \(x\in T\), where \(\varepsilon> 0\) is a parameter, \(T\) is a bounded domain in \(\mathbb{R}^ n\) with a smooth boundary and \(f(x)\) is a given smooth function ...
Ramm, A.G., Shifrin, E.I.
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Asymptotic behavior of solutions to nonlinear Volterra integral equations

Journal of Mathematical Analysis and Applications, 1984
Die Autoren untersuchen das asymptotische Verhalten für \(t\to \infty\) von Lösungen der nichtlinearen Volterra-Integralgleichung \[ \quad u(t)+\int^{t}_{0}b(t-s)Au(s)ds\ni F(t),\quad t\geq 0, \] wobei A ein abgeschlossener nichtlinearer akkretiver Operator in einem Banachraum ist.
Hulbert, Douglas S, Reich, Simeon
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Note on an asymptotic property of solutions to a class of Fredholm integral equations [PDF]

Quarterly of Applied Mathematics, 1970
Abstract : The note concerns a class of inhomogeneous integral equations of Fredholm's second kind on a semi-infinite interval. The dominating asymptotic behavior at infinity of the solution to such an equation is determined from the corresponding known asymptotic properties of its kernel and right-hand member. (Author)
Muki, R., Sternberg, E.
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Asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique II: Marginal perturbations and logarithmic corrections to the time decay of solutions [PDF]

Journal of Mathematical Physics, 2021
In this paper, we proceed with the analysis started in the work of Braga et al. [J. Math. Phys. 60(1), 013507, 2019] by the same authors, and using the renormalization group method, we obtain logarithmic corrections to the decay of solutions for a class of nonlinear integral equations whenever the nonlinearities are classified as marginal in the ...
Gastão A. Braga, Jussara M. Moreira, Camila F. Souza   +2 more
openaire   +3 more sources

Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics [PDF]

, 2013
We consider a semilinear elliptic problem [- \Delta u + u = (I_\alpha \ast \abs{u}^p) \abs{u}^{p - 2} u \quad\text{in (\mathbb{R}^N),}] where (I_\alpha) is a Riesz potential and (p>1).
Moroz, Vitaly, Van Schaftingen, Jean
core   +1 more source

Functional difference equations and eigenfunctions of a Schrödinger operator with δ′ −interaction on a circular conical surface

Proceedings of the Royal Society A, 2020
Eigenfunctions and their asymptotic behaviour at large distances for the Laplace operator with singular potential, the support of which is on a circular conical surface in three-dimensional space, are studied.
M. Lyalinov
semanticscholar   +1 more source