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Periodic solutions for systems with nonsmooth and partially coercive potential

Michael E. Filippakis (2006)

Archivum Mathematicum

In this paper we consider nonlinear periodic systems driven by the one-dimensional p -Laplacian and having a nonsmooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou...

Periodic solutions for third order ordinary differential equations

Juan J. Nieto (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.

Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia

A. Halanay (2012)

Mathematical Modelling of Natural Phenomena

Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem of Krasnoselskii....

Periodic solutions of an abstract third-order differential equation

Verónica Poblete, Juan C. Pozo (2013)

Studia Mathematica

Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation αu'''(t) + u''(t) = βAu(t) + γBu'(t) + f(t) with boundary conditions u(0) = u(2π), u'(0) = u'(2π) and u''(0) = u''(2π), where A and B are closed linear operators defined on a Banach space X, α,β,γ ∈ ℝ₊, and f belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel-Lizorkin spaces.

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