On the representation of the solutions of some strongly degenerating differential equation of second order in Hilbert space
In a separable Hilbert space H the equation (1) \(z\quad n(u''+Au)-c\quad 2u=0\) is studied. A is unbounded, self-adjoint and negative-definite operator in H with an everywhere dense domain D(A) in H. The compact inverse \(A^{-1}\) exists. A function u(z) for \(z>0\) and u(z)\(\in D(A)\) is a solution to (1) when this equation is satisfied in (0,\(\infty)\). A system of solutions to (1) is constructed and the asymptotic behaviour in the neighbourhood of \(z=0\) is studied. The results are obtained in a form of Laplace integrals and asymptotic series.
scientific article; zbMATH DE number 4056126
scientific article