@article{Slyusarchuk_2020, title={Equations in a Hilbert space whose solution sets are invariant with respect to a group isomorphic to a one-parameter group of unitary operators}, volume={72}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/687}, abstractNote={<p>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. <br>The applications of the obtained results to nonlinear mechanics are presented.</p> <p> </p>}, number={1}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Slyusarchuk, V. Yu.}, year={2020}, month={Jan.}, pages={86-99} }