Most texts on functional analysis (linear operator theory) deal almost exclusively with bounded, or continuous, operators. However, when one studies some problems on differential equations one needs to work with unbounded operators.

This book constitutes a good starting point to get acquainted with such operators, mostly with closed and strictly singular ones. It includes some applications to perturbation theory and ordinary differential equations, and gives some comments on the Dirichlet problem for PDE's. Finally, its extensive list of references motivates you to deeper study.
Read more at http://ebookee.org/Unbounded-Linear-Operators-Theory-and-Applications_201356.html#XYWWdpVXT1rViL4s.99