On the internal compactness of the space of regular solutions of one class of second order operator-differential equations with a discontinuous coefficient. (English) Zbl 07401982

Gasimova, Gunel M.

J. Contemp. Appl. Math. 11, No. 1, 90-96 (2021).

Summary: In paper given definition of the internal compactness of the space of regular solutions of one class of homogeneous operator-differential equations of second order with a discontinuous coefficient and found sufficient conditions for the internal compactness of these solutions.

MSC:

35B99	Qualitative properties of solutions to partial differential equations
35J15	Second-order elliptic equations
46C05	Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords:

Hilbert space; operator-differential equation; regular solution; internal compactness