On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length

Eduard Feireisl

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Displaying similar documents to “On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length”

Periodic solutions of a weakly nonlinear wave equation in $E_{3}$ in a spherically symmetrical case

Otto Vejvoda (1969)

Aplikace matematiky

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In the paper the conditions for the existence of a $2 π$ -periodic solution in $t$ of the system $u_{t t} - u_{r r} - (2 / r) u_{r} = ϵ f (t, r, u, u_{t}, u_{r})$ , $|u (t, 0)| < + \infty, u (t, π) = 0$ are investigated provided that $f$ is sufficiently smooth and $2 π$ -periodic in $t$ .

The existence of a periodic solution of a parabolic equation with the Bessel operator

Dana Lauerová (1984)

Aplikace matematiky

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In this paper, the existence of an $ω$ -periodic weak solution of a parabolic equation (1.1) with the boundary conditions (1.2) and (1.3) is proved. The real functions $f (t, r), h (t), a (t)$ are assumed to be $ω$ -periodic in $t, f \in L_{2} (S, H), a, h$ such that $a^{'} \in L_{\infty} (R), h^{'} \in L_{\infty} (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_{2} (S, V) \cap L_{\infty} (S, H)$ , has the derivative $u^{'} \in L_{2} (S, H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.

Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation

Věnceslava Šťastnová, Otto Vejvoda (1968)

Aplikace matematiky

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One investigates the existence of an $ω$ -periodic solution of the problem $u_{t} = u_{x x} + c u + g (t, x) + ϵ f (t, x, u, u_{x}, ϵ), u (t, 0) = h_{0} (t) + ϵ χ_{0} (t, u (t, 0), u (t, π)), u (t, π) = h_{1} (t) + ϵ χ_{1} (t, u (t, 0), u (t, π))$ , provided the functions $g, f, h_{0}, h_{1}, χ_{0}, χ_{1}$ are sufficiently smooth and $ω$ -periodic in $t$ . If $c \neq k^{2}$ , $k$ natural, such a solution always exists for sufficiently small $ϵ > 0$ . On the other hand, if $c = l^{2}$ , $l$ natural, some additional conditions have to be satisfied.

Solutions of the Dirac-Fock equations without projector

Éric Paturel (2000)

Journées équations aux dérivées partielles

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In this paper we prove the existence of infinitely many solutions of the Dirac-Fock equations with $N$ electrons turning around a nucleus of atomic charge $Z$ , satisfying $N < Z + 1$ and $α max (Z, N) < 2 / (2 / π + π / 2)$ , where $α$ is the fundamental constant of the electromagnetic interaction (approximately 1/137). This work is an improvement of an article of Esteban-Séré, where the same result was proved under more restrictive assumptions on $N$ .

Periodic solutions of evolution problem associated with moving convex sets

Charles Castaing, Manuel D.P. Monteiro Marques (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $- D u \in N_{C (t)} (u (t)) + f (t, u (t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C (t)} (u (t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions...

Weak Wecken's theorem for periodic points in dimension 3

Jerzy Jezierski (2003)

Fundamenta Mathematicae

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We prove that a self-map f: M → M of a compact PL-manifold of dimension ≥ 3 is homotopic to a map with no periodic points of period n iff the Nielsen numbers $N (f^{k})$ for k dividing n all vanish. This generalizes the result from [Je] to dimension 3.

Periodic solutions to a non-linear differential equation of the order $2n+1$

Monika Kubicova (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.

Existence of $T$ -periodic solutions for a class of lagrangian systems

Elvira Mirenghi, Maria Tucci (1990)

Rendiconti del Seminario Matematico della Università di Padova

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Periodic solutions to a non-linear differential equation of the order $2n+1$

Monika Kubicova (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.