Results 111 to 120 of about 179,434,279 (151)

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 ...
Olmstead, W. E., Handelsman, Richard A.
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Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

Acta Mathematica Vietnamica, 2015
The authors study the following integral equation \[ x(t)=V\left(t,x(t),\int_0^{\mu_1(t)}V_1\left(t,s,x\left(\sigma_1(s)\right),\int_0^{\mu_2(s)}V_2\left(t,s,r,x\left(\sigma_2(r)\right)\right)\, dr\right)\, ds\right) \] \[ +\int_0^{\infty}F\left(t,s,x\left(\chi_1(s)\right),\hdots,x\left(\chi_q(s)\right),\int_0^{\mu_3(s)}F_1\left(t,s,r,x\left(\sigma_3(r)
Ngoc, L. T. P., Long, N. T.
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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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Asymptotic analysis of the Marchenko integral equation and soliton asymptotics of a solution of the nonlinear schrödinger equation

Physica D: Nonlinear Phenomena, 1995
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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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Periodic and asymptotically periodic solutions of Volterra integral equations

Funkcialaj Ekvacioj, 1996
The paper deals with integral equations of the form \[ x(t) = a(t) - \int^t_0 D \bigl( t,s,x(s) \bigr)ds, \] \[ x(t)= a(t)- \int^t_{-\infty} D\bigl(t,s,x(s) \bigr)ds, \] and \[ x(t) = p(t)-\int^t_{-\infty} P\bigl(t,s,x(s)\bigr)ds, \] in which \(p\) is \(T\)-periodic, \(P(t+T, s+T.x) = P(t,s,x)\), and \(a(t)\) and \(D(t,s,x)\) convergent to \(p(t)\) and
Burton, T. A., Furumochi, Tetsuo
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On the Oscillatory and Asymptotic Behavior of Solutions of Certain Integral Equations

Mediterranean Journal of Mathematics, 2016
The author studies the long time behavior of the solution of a 1D integral equation with fractional powers and non-locally vanishing and nonlinear weights. He shows that under some long time behavior of the weights, the solution is dominated by the source term, i.e., the term coming from the integral equation is indeed dominated by the source term. The
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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.
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Bell Polynomials in the Mathematica System and Asymptotic Solutions of Integral Equations

Theoretical and Mathematical Physics, 2019
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Marichev, O. I., Slavyanov, S. Yu., Brychkov, Yu. A.   +2 more
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