PROC
On positive solutions of nonlinear fractional differential equations
Daria Bugajewska Mirosława Zima
Conference Publications 2003, 2003(Special): 141-146 doi: 10.3934/proc.2003.2003.141
The aim of this note is to prove some existence and uniqueness theorems on positive solutions of some nonlinear fractional equations. Classical as well as Carathéodory’s solutions are under our considerations.
keywords: Keywords and Phrases
PROC
On the spectral radius of linearly bounded operators and existence results for functional-differential equations
Daria Bugajewska Mirosława Zima
Conference Publications 2003, 2003(Special): 147-155 doi: 10.3934/proc.2003.2003.147
In this paper we formulate conditions, different from the global commutativity, under which one can estimate the spectral radius of the composition of linearly bounded operators. We apply this estimation to prove the existence of global solutions for some functional differential equations and systems of such equations. All our results are illustrated by suitable examples.
keywords: functional partial differential equation system of differential equations of neutral type. linearly bounded operator existence of global solutions spectral radius differential equations with maxima
DCDS
Lyapunov stability for regular equations and applications to the Liebau phenomenon
Feng Wang José Ángel Cid Mirosława Zima
Discrete & Continuous Dynamical Systems - A 2018, 38(9): 4657-4674 doi: 10.3934/dcds.2018204

We study the existence and stability of periodic solutions of two kinds of regular equations by means of classical topological techniques like the Kolmogorov-Arnold-Moser (KAM) theory, the Moser twist theorem, the averaging method and the method of upper and lower solutions in the reversed order. As an application, we present some results on the existence and stability of $ T$-periodic solutions of a Liebau-type equation.

keywords: Lyapunov stability regular equation Liebau phenomenon KAM theory Moser twist theorem

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