Geodesic
On the Solvability of the Boundary-Value Problem for Second-Order Equations in Hilbert Space with an Operator Coefficient in the Boundary Condition
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 861-869.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the boundary-value problem on a finite interval for a class of second-order operator-differential equations with a linear operator in one of its boundary conditions. We obtain sufficient conditions for the regular solvability of the boundary-value problem under consideration; these conditions are expressed only in terms of its operator coefficients.
Keywords: second-order operator-differential equation, boundary-value problem, Hilbert space, self-adjoint operator, square-integrable function, linear bounded operator, Banach inverse-operator theorem. 
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S. S. Mirzoev; M. Yu. Salimov. On the Solvability of the Boundary-Value Problem for Second-Order Equations in Hilbert Space with an Operator Coefficient in the Boundary Condition. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 861-869. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a6/

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