Well-posedness of the second-order linear singular Dirichlet problem

Abstract

Abstract Conditions guaranteeing well-posedness of the problem u ' ' = p 0 ( t ) u + q 0 ( t ) ${u^{\prime \prime }=p_0(t)u+q_0(t)}$ , u ( a ) = 0 ${u(a)=0}$ , u ( b ) = 0 ${u(b)=0}$ , are established. Here p 0 , q 0 : ] a , b [ → ℝ ${p_0,q_0\colon ]a,b[\rightarrow \mathbb {R}}$ are locally Lebesgue integrable functions and may have singularities at t = a ${t=a}$ and t = b ${t=b}$ .