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

• Дата: 2020
• Автори: Slyusarchuk, V. Yu., Слюсарчук, В. Ю.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2020
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/687
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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...