Results 81 to 90 of about 585 (118)

VOLTERRA INTEGRAL EQUATIONS AND NONLINEAR SEMIGROUPS

Nonlinear Analysis: Theory, Methods & Applications, 1977
Publisher Summary This chapter discusses Volterra integral equations and nonlinear semigroups. It presents the nonlinear Volterra integral equation x ( t ) = y ( t ) + ∫ g ( t − s , x ( s )) ds , t ≥ 0, where H is a Hilbert space, y : [0, ∞) → H is given, g : [0, ∞) × H → satisfies a Lipschitz condition in its second place, and x :
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Nontrivial Solutions to Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximate solutions of nonlinear two‐dimensional Volterra integral equations

Mathematical Methods in the Applied Sciences, 2021
The present work is concerned with examining the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two‐dimensional Volterra integral equations (2D‐VIEs). The result obtained by the suggested method for linear 2D‐VIEs is compared with the differential transform method, Bernstein polynomial method, and piecewise block‐plus method and ...
Sumbal Ahsan, Rashid Nawaz, Muhammad Akbar, Kottakkaran Sooppy Nisar, Dumitru Baleanu   +4 more
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Nonlinear volterra integral equations of the first kind

Nonlinear Analysis: Theory, Methods & Applications, 1995
Consider the weakly singular Volterra systems of the first kind \[ \int_0^t {k \bigl( t,s,x(s) \bigr) \over (t - s)^\alpha} ds = f(t), \qquad t \in J = [0,a], \tag{*} \] where \(\alpha \in [0,1)\), \(k : \Delta \times \mathbb{R}^n \to \mathbb{R}^n\) with \(\Delta = \{(s,t) \in J^2 : s \leq t\}\) and \(f : J \to \mathbb{R}^n\) are given.
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Nonlinear Volterra Integral Equations

2011
It is well known that linear and nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics, and semi-conductor devices. Volterra started working on integral equations in 1884, but his serious study began in 1896. The name integral equation was given by du Bois-Reymond in 1888.
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On nonlinear Fredholm–Volterra integral equations with hysteresis

Applied Mathematics and Computation, 2004
The author improves his earlier result concerning the existence and uniqueness of solutions of the following Fredholm-Volterra system with hysteresis \[ x(t)= g(t)+ \int^t_0 p(t,s)\phi(s, x(s), w[S[x]](s))\,ds+ \int^\infty_0 q(t,s) \psi(s, x(s), w[S[x]](s))\,ds,\tag{1} \] where \(w\) denotes a hysteresis operator and \(S\) is the superposition operator
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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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Modified decomposition method for nonlinear Volterra–Fredholm integral equations

Chaos, Solitons & Fractals, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bildik, Necdet, Inc, Mustafa
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Generalized solutions to nonlinear Volterra integral equations with non-Lipschitz nonlinearity

Nonlinear Analysis: Theory, Methods & Applications, 1999
For a nonlinear Volterra equation of the second kind approximate solutions are studied. These are (unique smooth) solutions of a family of associated Volterra equations where the kernel and the known function is ``regularized''. Under an equivalence relation, this family of solutions may be interpreted as a generalized function which (under additional ...
Pilipović, Stevan, Stojanović, Mirjana
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Block methods for nonlinear Volterra integral equations

BIT, 1975
A method used to solve linear Fredholm equations is adapted to obtain a generalization of block methods for solving nonlinear Volterra integral equations. Conditions for such methods to be convergent andA-stable are given along with some numerical examples.
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