Results 131 to 140 of about 755 (165)

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
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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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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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Taylor polynomial solutions of nonlinear Volterra–Fredholm integral equations

Applied Mathematics and Computation, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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