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On periodic motions of a two dimensional Toda type chain

Gianni Mancini, P. N. Srikanth (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, i.e. ϕ t t i - ϕ x x i = exp ( ϕ i + 1 - ϕ i ) - exp ( ϕ i - ϕ i - 1 ) 0 < x < π , t , i ( T C ) ϕ i ( 0 , t ) = ϕ i ( π , t ) = 0 t , i . We consider the case of “closed chains” i.e. ϕ i + N = ϕ i i and some N and look for solutions which are peirodic in time. The existence of periodic solutions for the dual problem is proved in Orlicz space setting.

On periodic motions of a two dimensional Toda type chain

Gianni Mancini, P. N. Srikanth (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, i.e. ϕ t t i - ϕ x x i = exp ( ϕ i + 1 - ϕ i ) - exp ( ϕ i - ϕ i - 1 ) 0 < x < π , t I R , i Z Z ( TC ) ϕ i ( 0 , t ) = ϕ i ( π , t ) = 0 t , i . We consider the case of “closed chains" i.e. ϕ i + N = ϕ i i Z Z and some N I N and look for solutions which are peirodic in time. The existence of periodic solutions for the dual problem is proved in Orlicz space setting.

On periodic solutions of non-autonomous second order Hamiltonian systems

Xingyong Zhang, Yinggao Zhou (2010)

Applications of Mathematics

The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system u ¨ ( t ) = F ( t , u ( t ) ) , a.e. t [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . Some new existence theorems are obtained by the least action principle.

On solvability of nonlinear operator equations and eigenvalues of homogeneous operators

Věra Burýšková, Slavomír Burýšek (1996)

Mathematica Bohemica

Notions as the numerical range W ( S , T ) and the spectrum ( S , T ) of couple ( S , T ) of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation S x - l T x = y . Conditions for the existence of eigenvalues of the couple ( S , T ) are given.

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