Results 161 to 170 of about 3,846,782 (204)

Nonlinear Volterra Integral Equations and the Apéry Identities

Bulletin of the London Mathematical Society, 1992
The authors study necessary and sufficient conditions for the existence of nontrivial solutions of the Volterra integral equation \(u(x)=\int_ 0^ x k(x-s) g(u(s))ds\). Using the identity \[ \begin{multlined} \int_ a^ x f(s)h(s)ds= \int_ a^ \lambda f(s)\varphi(s)ds+ \int_ a^ \lambda [f(\lambda-f(s)][\varphi(s)-h(s)]ds+\\ +\int_ \lambda^ x [f(s)- f ...
Bushell, P. J., Okrasiński, W.
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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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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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NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS

Bulletin of the London Mathematical Society, 2003
Some new results concerning the existence and uniqueness of nontrivial solutions to the title equations are presented.
Mydlarczyk, W., Okrasiński, W.
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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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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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Nontrivial Solutions to Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1991
The Volterra integral equation \[ u(x) = \int_0^x {k(x - s)g(u(s))ds\quad (x > 0)} \] is considered, where $x \geqq 0$ is a monotonic integrable function and g is an increasing, continuous function such that $g(0) = 0$. Some necessary and sufficient conditions for the existence of nontrivial solutions to the above equation are presented.
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Collocation methods for nonlinear stochastic Volterra integral equations

Computational and Applied Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoli Xu, Yu Xiao, Haiying Zhang
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On a Nonlinear Volterra Integral Equation on a Hilbert Space

SIAM Journal on Mathematical Analysis, 1977
Nonlinear Volterra integral equations with singular kernels are considered. The existence and the asymptotic behavior of solutions is studied in a special case.
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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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