We consider on the positive half-line an equation of the kindx''+cx'=a(t)V'(x) and prove, by variational arguments, the existence of a solution which fulfils the boundary conditions x(0)=0, x(+\infty)=1. The constant c is non-negative and a(t) belongs to a certain class of positive functions. The existence of such a solution in the case c=0 means that the system behaves in a significantly different way from its autonomous counterpart.
On a class of bounded trajectories for some non-autonomous systems / Gavioli, Andrea; L., Sanchez. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 281:11(2008), pp. 1557-1565. [10.1002/mana.200510696]
On a class of bounded trajectories for some non-autonomous systems
GAVIOLI, Andrea;
2008
Abstract
We consider on the positive half-line an equation of the kindx''+cx'=a(t)V'(x) and prove, by variational arguments, the existence of a solution which fulfils the boundary conditions x(0)=0, x(+\infty)=1. The constant c is non-negative and a(t) belongs to a certain class of positive functions. The existence of such a solution in the case c=0 means that the system behaves in a significantly different way from its autonomous counterpart.
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