On a generalization of the Osgood condition.

Mydlarczyk, W.; Okrasiński, W.

Displaying similar documents to “On a generalization of the Osgood condition.”

A Liapunov functional for a linear integral equation.

Burton, T.A. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Volterra and Urysohn integral equations in Banach spaces.

O'Regan, Donal (1998)

Journal of Applied Mathematics and Stochastic Analysis

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Resolvents, integral equations, limit sets

Theodore Allen Burton, D. P. Dwiggins (2010)

Mathematica Bohemica

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In this paper we study a linear integral equation $x (t) = a (t) - \int_{0}^{t} C (t, s) x (s) d s$ , its resolvent equation $R (t, s) = C (t, s) - \int_{s}^{t} C (t, u) R (u, s) d u$ , the variation of parameters formula $x (t) = a (t) - \int_{0}^{t} R (t, s) a (s) d s$ , and a perturbed equation. The kernel, $C (t, s)$ , satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of $C$ and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.

On the Volterra integral equation with weakly singular kernel

Stanisław Szufla (2006)

Mathematica Bohemica

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We give sufficient conditions for the existence of at least one integrable solution of equation $x (t) = f (t) + \int_{0}^{t} K (t, s) g (s, x (s)) d s$ . Our assumptions and proofs are expressed in terms of measures of noncompactness.

On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.

Chen, Lian-Ying, Zhao, Chang-Jian, Cheung, Wing-Sum (2010)

Journal of Inequalities and Applications [electronic only]

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Integral equations with contrasting kernels.

Burton, T.A. (2008)

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On the solutions of $n$ -th order nonlinear differential equation in $L^{2} (0, \infty)$

Jozef Eliáš (1982)

Mathematica Slovaca

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Weak and strong topologies and integral equations in Banach spaces

Donal O'Regan (1995)

Annales Polonici Mathematici

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The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of $L^{α}$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.

Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici

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A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.