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Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integrodifferential Equations.

R. Vermiglio (1988)

Numerische Mathematik

Near-best approximations to the solution of Fredholm integral equation of the second kind

David Levin (1982)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales

Youssef N. Raffoul (2016)

Archivum Mathematicum

In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.

Necessary and sufficient well-posedness conditions for a convolution equation of the second kind with even kernel on a finite interval.

Voronin, A.F. (2008)

Sibirskij Matematicheskij Zhurnal

Neural networks with memory.

Burton, T.A. (1991)

Journal of Applied Mathematics and Stochastic Analysis

New conditions for the existence of non trivial solutions to some Volterra equations.

W. Okrasinski (1990)

Extracta Mathematicae

We consider the following Volterra equation:(1) u(x) = ∫0x k(x-s) g(u(s)) ds, where,k: [0, δ0] → R is an increasing absolutely continuous function such thatk(0) = 0g: [0,+ ∞) → [0,+ ∞) is an increasing absolutely continuous function such that g(0) = 0 and g(u)/u → ∞ as u → 0+ (see [3]).Let us note that (1) has always the trivial solution u = 0.Some necessary and sufficient conditions for the existence of nontrivial solutions to (1) with k(x) = xα - 1 (α>0) are given in [1], [2] and...

New convergence criteria for the Newton-Kantorovich method and some applications to nonlinear integral equations

Espedito De Pascale, Pjotr P. Zabrejko (1998)

Rendiconti del Seminario Matematico della Università di Padova

New existence results and comparison principles for impulsive integral boundary value problem with lower and upper solutions in reversed order.

Wang, Guotao, Zhang, Lihong, Song, Guangxing (2011)

Advances in Difference Equations [electronic only]

New integral inequalities for iterated integrals with applications.

Agarwal, Ravi P., Ryoo, Cheon Seoung, Kim, Young-Ho (2007)

Journal of Inequalities and Applications [electronic only]

New retarded integral inequalities with applications.

Agarwal, Ravi P., Kim, Young-Ho, Sen, S.K. (2008)

Journal of Inequalities and Applications [electronic only]

New spectral criteria for almost periodic solutions of evolution equations

Toshiki Naito, Nguyen Van Minh, Jong Son Shin (2001)

Studia Mathematica

We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where $\bar{e^{i s p (f)}}$ may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...

Non local solutions of a nonlinear hyperbolic partial differential equation.

Lopes Frota, Cícero (1994)

Portugaliae Mathematica

Non-autonomous implicit integral equations with discontinuous right-hand side

Giovanni Anello, Paolo Cubiotti (2004)

Commentationes Mathematicae Universitatis Carolinae

We deal with the implicit integral equation $h (u (t)) = f (t, \int_{I} g (t, z) u (z) d z) for a.a. t \in I,$ where $I : = [0, 1]$ and where $f : I \times [0, λ] \to ℝ$ , $g : I \times I \to [0, + \infty [$ and $h :] 0, + \infty [\to ℝ$ . We prove an existence theorem for solutions $u \in L^{s} (I)$ where the contituity of $f$ with respect to the second variable is not assumed.

Non-autonomous vector integral equations with discontinuous right-hand side

Paolo Cubiotti (2001)

Commentationes Mathematicae Universitatis Carolinae

We deal with the integral equation $u (t) = f (t, \int_{I} g (t, z) u (z) d z)$ , with $t \in I : = [0, 1]$ , $f : I \times ℝ^{n} \to ℝ^{n}$ and $g : I \times I \to [0, + \infty [$ . We prove an existence theorem for solutions $u \in L^{s} (I, ℝ^{n})$ , $s \in] 1, + \infty]$ , where $f$ is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where $f$ does not depend explicitly on the first variable $t \in I$ .

Currently displaying 1 – 20 of 82