On Boundary Conditions for Sturm-Liouville Differential Operators in the Direct Sum Spaces

On the domain of selfadjoint extension of the product of Sturm‐Liouville differential operators

“…This characterization is an extension of those by Everitt and Zettl [4] and those in [5,6,7,10,11,12,13].…”

“…We begin with a brief summary of adjoint pairs of operators and products operators (a full treatment may be found in [2,Chapter III] and [3,4,5,7,8,9]). …”

“…where τ + is the formal, or Lagrangian, adjoint of τ given by [7,8,9,10]. In the regular problem, the minimal operator T 0 (τ) is the restriction of…”

“…Similarly, b is LC means that all solutions of (2.4) are in L 2 w (α, b), a < α < b. This classification is independent of λ in (2.4), (see [7,10,13,18]). Otherwise, b is LP.…”

“…where D 0 (τ), N + , and N − are linearly independent subspaces and the sum is direct (which we indicate with the symbol +), see [2,5,7,13]. Any selfadjoint extension S of the symmetric differential operator T 0 (τ) satisfies…”