Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 101, pp. 1-16.

Title: Formally self-adjoint quasi-differential operators and
       boundary-value problems
        
Authors: Andrii Goriunov (National Academy of Sciences, Kyiv, Ukraine)
         Vladimir Mikhailets (National Academy of Sciences, Kyiv, Ukraine)
         Konstantin Pankrashkin (Univ. Paris-Sud 11, Orsay, France)

Abstract:
 We develop the machinery of boundary triplets for one-dimensional operators
 generated by formally self-adjoint quasi-differential expression of arbitrary
 order on a finite interval. The technique is then used to describe
 all maximal dissipative, accumulative and self-adjoint extensions of the
 associated minimal operator and its generalized resolvents in terms
 of the boundary conditions. Some specific classes are considered in greater
 detail.

Submitted March 6, 2013. Published April 19, 2013.
Math Subject Classifications: 34B05, 34L40, 47N20, 34B37.
Key Words: Quasi-differential operator; distributional coefficients;
           self-adjoint extension; maximal dissipative extension; 
           generalized resolvent.