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Information × Registration Number 0212U002005, 0111U000481 , R & D reports Title Local, global and asymptotic properties of solutions of singular, spectral and nonclassical problems for elliptic and evolution equations and variational inequalities popup.stage_title Head Kovalevsky Alexander Al'bertovich, Shishkov Andrey Evgenievich, Registration Date 12-01-2012 Organization Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine popup.description2 The notion of solution of degenerate anisotropic variational inequality of second-order with weakly integrable right-hand side and the set of constraints lying in a functional class which does not belong to Sobolev spaces is introduced. The existence and uniqueness of this solution are proved. The Dirichlet problem for semi-linear elliptic second-order equations with superlinear absorption term is investigated. Strict necessary and sufficient conditions on the character of degeneration of the corresponding absorption potential which guarantee the existence of singular on boundary of the domain nonnegative solutions and solutions with infinite Dirichlet data on the whole boundary of the domain are established. The existence of very weak solutions (e.g. solutions in Morrey spaces) of nonlinear elliptic systems is proved. We find conditions of absence of the uniqueness of solution in the analytical statement of the Dirichlet problem for the equation of vibration of a string in some domains with unbounded boundary. These conditions correspond to the nonstandard location of conics in the Poncelet problem. Spectral properties of the Schrodinger operator with infinite number of point interactions are investigated. We find configurations of points for which every realization of the Schrodinger operator has absolutely continuos nonnegative spectrum. Product Description popup.authors Бурський Володимир Петрович Войтович Михайло Володимирович Голощапова Наталя Іванівна Каліта Євген Олександрович Карабаш Ілля Михайлович Костенко Олексій Сергійович Лесіна Євгенія Вікторівна Маламуд Марк Михайлович Намлєєва Юлія Валеріївна Рудакова Ольга Анатоліївна popup.nrat_date 2020-04-02 Close