Square integrable solutions of 𝐿𝑦=𝑓(𝑡,𝑦)

Abstract

Let L L be an ordinary linear differential operator and L + {L^ + } its formal adjoint. It is shown that, under suitable conditions on f f , all solutions of L y = f ( t , y ) Ly = f(t,y) are in L 2 ( 0 , ∞ ) {L^2}(0,\infty ) provided that all those of L y = 0 Ly = 0 and L + y = 0 {L^ + }y = 0 are.