Equations in a Hilbert space whose solution sets are invariant with respect to a group isomorphic to a one-parameter group of unitary operators

  • V. Yu. Slyusarchuk Nat. Univ. farms and nature management, Rivne
Keywords: Hilbert space, 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.

 

Author Biography

V. Yu. Slyusarchuk, Nat. Univ. farms and nature management, Rivne

Василь Юхимович

References

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Published
15.01.2020
How to Cite
SlyusarchukV. Y. “Equations in a Hilbert Space Whose Solution Sets Are Invariant With Respect to a Group Isomorphic to a One-Parameter Group of Unitary Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 1, Jan. 2020, pp. 86-99, https://umj.imath.kiev.ua/index.php/umj/article/view/687.
Section
Research articles