Browsing by Author "Zhosybayeva B."

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    On existence of a solution of a class of second order differential equations
    (Faculty of engineering and natural sciences, 2019) Zhosybayeva B.
    The paper was devoted to the study of issues on the existence and compactness of a resolvent, as well as estimates of the distribution function of singular numbers (s-numbers) of a differential operator of mixed type in a noncompact domain. We used the embedding theorems for Sobolev-type weighted spaces, the method of a priori estimates, the uniform localization method. In this paper, besides the above methods, an approach is proposed that allows one to find two-sided estimates of singular numbers (approximation numbers, s-numbers) of differential operators containing a sign-changing parameter. As a result of the study, the following results were obtained for a class of mixed-type differential operators defined in a noncompact domain: a theorem on the existence of a bounded inverse operator was proved: a theorem on the compactness (discreteness of the spectrum) of the resolvent of a mixed-type operator was proved; a conditions to the two-sided estimate for the distribution function of singular numbers (s-numbers) of the resolvent of a mixed-type differential operator given in an unbounded domain are obtained.