Results 91 to 100 of about 585 (118)

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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ON OPTIMAL CONTROL FOR NONLINEAR VOLTERRA-STIELTJES INTEGRAL EQUATIONS

IFAC Proceedings Volumes, 1983
Abstract Some results concerning the optimal control for measure differ-ential equations are generalized to the case of Volterra equations. Because of a suitable non-anticipative version of the underlying system equation, already the usual Lipschitz condition guarantees the existence of a unique solution.
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Nonlinear Volterra integral equations and the Schröder functional equation

Nonlinear Analysis: Theory, Methods & Applications, 2011
The author shows an interesting connection between a special class of Volterra integral equations with convolution kernels \[ u(t)=\int\limits_{0}^{t}k(t-s)g(u(s)ds, \quad g(0)=0, \quad t\geq 0, \] and the famous Schröder equation \[ F(h(x))=cF(x),\quad x\in I.
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On a Nonlinear Volterra-Fredholm Integral Equation

Sarajevo Journal of Mathematics
In this paper we study the existence, uniqueness and other properties of solutions of a certain nonlinear Volterra-Fredholm integral equation. The well known Banach fixed point theorem and the new integral inequality with explicit estimate are used to establish the results.   2000 Mathematics Subject Classification.
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A new general integral transform for solving integral equations

Journal of Advanced Research, 2021
Hossein Jafari
exaly  

BINN: A deep learning approach for computational mechanics problems based on boundary integral equations

Computer Methods in Applied Mechanics and Engineering, 2023
Jia Sun, 一铮 王, Zhenhan Yao
exaly  

Nonlinear Volterra Integral Equations

2015
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Nonlinear Volterra Integral Equations with Convolution Kernel

Journal of the London Mathematical Society, 1990
P. J. Bushell, W. Okrasinski
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Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations

Mathematics and Computers in Simulation, 2005
Mohsen Razzaghi
exaly  

Nonlinear Volterra integral equation with discontinuous right-hand side

1996
The author proves a theorem about the existence of a continuous solution of the nonlinear Volterra integral equation \[ x(t)= u(t)+ \int_0^t f(t,\tau,x(\tau)) d\tau, \] in the case where the function \(f\) is nondecreasing and continuous from the right in its third variable. In addition to some measurability assumptions it is assumed that \(|f(t,\tau,x)
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