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On the asymptotic solution of a nonlinear Volterra integral equation [PDF]

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971
A technique based on the analytic continuation and study of the pole diagram of the Mellin transform has been described for obtaining asymptotic solution of nonlinear Volterra type integral equations for small and large values of the argument. Solutions to a number of problems in nonlinear heat conduction and boundary-layer heat transfer have been ...
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Asymptotics of the solutions of integral equations with a difference kernel [PDF]

Ukrainian Mathematical Journal, 1982
\textit{S. Karlin} [Pac. J. Math. 5, 229-257 (1955; Zbl 0067.349)] considered equations of the form \[ (1)\quad u(\xi)-\int^{\infty}_{- \infty}u(\xi -t)dF(t)=g(\xi),\quad ...
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Asymptotic Solution to a Class of Nonlinear Volterra Integral Equations. II

SIAM Journal on Applied Mathematics, 1972
It is known that the nonlinear Volterra integral equation \[ \varphi (t)\pi ^{( - 1 / 2)} \,\int_0^t (t - s)^{{ - 1 / 2} } [ {f(s) - \varphi ^n (s)} ]ds,\quad t\geqq 0,\geqq n\geqq 1,\] has a continuous solution $\varphi (t) \geqq 0$ which is unique for each bounded and locally lntegrable function $f(t) \geqq 0$ Our prior investigation considered the ...
Richard A. Handelsman, W. E. Olmstead
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Asymptotic Solution of Palm's Integral Equation

Operations Research, 1963
The asymptotic solution of Palm's nonlinear integral equation is obtained, valid for channels sufficiently far away from the first channel. It is shown how the asymptotic formula may be applied, in certain cases, for the determination of the number of channels sufficient to serve a given Poisson input.
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On the Asymptotic Solution to a Class of Linear Integral Equations

SIAM Journal on Applied Mathematics, 1988
The author obtains complete uniform asymptotic expansions of the solutions to the integral equations \(Ku=f(x),\) and \(L_ xL^*_ XKu=f(x ...
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On existence and asymptotic behaviour of solutions of a functional integral equation

Nonlinear Analysis: Theory, Methods & Applications, 2007
Q1
Józef Banaś, Ignacio J. Cabrera
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Asymptotic solutions of integral equations with a convolution kernel. I

Journal of Mathematical Physics, 1973
Homogeneous eigenvalue problems for integral equations with a kernel of the convolution type, defined on a finite volume in N-dimensional space, are discussed. It is shown that they can be reduced asymptotically to eigenvalue problems for simpler integral equations.
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Asymptotic Solutions of Some Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1981
The asymptotic behavior of solutions of three nonlinear Volterra integral equations of the form $u(t) + \int_0^t {A(t - s)g(u(s))ds = 0} $ is studied. These equations arise from certain diffusion problems, in dimensions 1, 2 or 3, with nonlinear boundary conditions.
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Asymptotic Solution of a Class of Strongly Singular Integral Equations

SIAM Journal on Applied Mathematics, 1990
A class of strongly singular, nonlinear integral equations is considered and sufficient conditions for the uniqueness of the solution and, in the linear and homogeneous case, the nonpositiveness of the associated eigenvalues are obtained. When the singular integral is proportional to a small perturbation parameter, a procedure for the construction of ...
Muneo Hori, Siavouche Nemat-Nasser
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Higher-dimensional nonlinear integrable equations: Asymptotics of solutions and perturbations

Journal of Mathematical Sciences, 2005
The survey is devoted to the analysis of solutions of (2+1)D integrable equations -- Kadomtsev-Petviashvili, Davey-Stewartson, Ishimori ones. Using the inverse scattering transform method the author studies temporal asymptotics of decreasing solutions and formal asymptotic solutions for perturbations of solutions to Davey-Stewartson equations.
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