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Equations containing locally Henstock-Kurzweil integrable functions

Seppo Heikkilä, Guoju Ye (2012)

Applications of Mathematics

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

Equations in differentials in the algebra of generalized stochastic processes

Nadzeya V. Bedziuk, Aleh L. Yablonski (2010)

Banach Center Publications

We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes is...

Estimates for the Cauchy matrix of perturbed linear impulsive equation.

Simeonov, P.S., Bajnov, D.D. (1994)

International Journal of Mathematics and Mathematical Sciences

Estimates of solutions of impulsive parabolic equations and applications to the population dynamics.

Drumi Bainov, Emil Minchev (1996)

Publicacions Matemàtiques

A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.

Estimates of the solutions of impulsive quasilinear functional differential equations

Drumi Bainov, Valéry Covachev, Ivanka Stamova (1991)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Existence and global asymptotical stability of periodic solution for the $T$ -periodic logistic system with time-varying generating operators and $T_{0}$ -periodic impulsive perturbations on Banach spaces.

Wang, Jinrong, Xiang, X., Wei, W., Chen, Qian (2008)

Discrete Dynamics in Nature and Society

Existence and positivity of solutions for a nonlinear periodic differential equation

Ernest Yankson (2012)

Archivum Mathematicum

We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.