Equations in a Hilbert space whose solution sets are invariant with respect to a group isomorphic to a one-parameter group of unitary operators
Abstract
We construct classes of equations in a Hilbert space whose sets of solution are invariant with respect to a group isomorphic to a one-parameter group of unitary operators. It is shown that the unbounded solutions of these equations are unstable.
The applications of the obtained results to nonlinear mechanics are presented.
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