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On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Wenjie Gao, Junyu Wang (1995)

Annales Polonici Mathematici

The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces

Zuomao Yan (2011)

Annales Polonici Mathematici

This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.

On a parabolic integrodifferential equation of Barbashin type

B. G. Pachpatte (2011)

Commentationes Mathematicae Universitatis Carolinae

In the present paper we study some basic qualitative properties of solutions of a nonlinear parabolic integrodifferential equation of Barbashin type which occurs frequently in applications. The fundamental integral inequality with explicit estimate is used to establish the results.

On a perturbed nonlinear third order differential equation

Michal Greguš (1997)

Archivum Mathematicum

In this paper we will study some asymptotic properties of a nonlinear third order differential equation viewed as a perturbation of a simpler nonlinear equation investigated recently by the authors in [4].

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