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

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 L 2 ( S , H ) , a , h such that a ' L ( R ) , h ' L ( R ) and they fulfil (3). The solution u belongs to the space L 2 ( S , V ) L ( S , H ) , has the derivative u ' 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 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 .