Shakhmurov, Veli B.2024-05-252024-05-2520190035-75961945-379510.1216/RMJ-2019-49-5-16472-s2.0-85072712288https://doi.org/10.1216/RMJ-2019-49-5-1647https://hdl.handle.net/20.500.14517/1486We study separability and spectral properties of singular degenerate elliptic equations in vector-valued L-p spaces. We prove that a realization operator according to this equation with some boundary conditions is separable and Fredholm in L-p. The leading part of the associated differential operator is not self-adjoint. The sharp estimate of the resolvent, discreteness of spectrum and completeness of root elements of this operator is obtained. Moreover, we show that this operator is positive and generates a holomorphic C-0-semigroups on L-p. In application, we examine the regularity properties of nonlocal boundary value problem for degenerate elliptic equation and for the system of degenerate elliptic equations of either finite or infinite number.eninfo:eu-repo/semantics/openAccessSeparable differential operatorsspectral properties of differential operatorsdegenerate differential equationsabstract differential equationsArticleQ3Q349516471666WOS:0004866083000100