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On discreteness of spectrum and positivity of the Green's function for a second order functional-differential operator on semiaxis
Boundary Value Problems
We study conditions of discreteness of spectrum of the operator defined by . The operator has two singularities at the ends of the interval (0, ∞). The second question is positivity of solutions of the equation Lu = f under boundary conditions u(0) = 0, u (∞) = 0. The used abstract scheme is close to the well-known MS Birman's method in the spectral theory of self-adjoint operators. Conditions for discreteness of spectrum and positivity of the Green's operator are obtained. The result relatesdoi:10.1186/1687-2770-2014-102 fatcat:deirfdngy5ae5g6yyzw2k2sgci