A remark on non-linear integral equations of the Hammerstein type
A shooting method for singular nonlinear second order Volterra integro-differential equations.
A singular initial value problem for the equation
We consider the problem of the existence of positive solutions u to the problem , (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
A stability result for a class of nonlinear integrodifferential equations with L¹ kernels
We study second order nonlinear integro-differential equations in Hilbert spaces with weakly singular convolution kernels obtaining energy estimates for the solutions, uniform in t. Then we show that the solutions decay exponentially at ∞ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
A Unified Approach for Constructing Fast Two-Step Newton-like Methods.
A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators
We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.
A Volterra inequality with the power type nonlinear kernel.
About the existence of integrable solutions of a functional-integral equation.
We improve (in some sense) a recent theorem due to Banas and Knap (1989) about the existence of integrable solutions of a functional-integral equation.
Addendum to “Integrable and continuous solutions of a nonlinear quadratic integral equation”.
Algunas Aproximaciones Sucesivas Para Las Aplicaciones En La Clase D (a,b).
An abstract inverse problem.
An abstract nonlinear second order differential equation
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
An approximate solution of some Volterra integral equation with a smooth kernel
The behaviour near the origin of nontrivial solutions to integral Volterra equations with a power nonlinearity is studied. Estimates of nontrivial solutions are given and some numerical examples are considered.
An existence theorem for a Volterra integral equation with deviating arguments.
An existence theorem for an implicit integral equation with discontinuous right-hand side.
An existence theorem for Hammerstein integral equations.
An existence theorem for the Urysohn integral equation in Banach spaces
An existence theorem for Volterra integrodifferential equations with infinite delay.
An Extrapolation Method with Step Size Control for Nonlinear Volterra Integral Equations.
An improved exponential decay result for some semilinear integrodifferential equations
We prove exponential decay for the solution of an abstract integrodifferential equation. This equation involves coefficients of polynomial type, weakly singular kernels as well as different powers of the unknown in some norms.