Structure and asymptotic expansion of eigenvalues of an integral-type nonlocal problem (Q2832425)

The authors are concerned with the eigenvalue linear problem with one-sided integral condition: NEWLINE\[NEWLINE -y''(x)+q(x)y(x)=\lambda y(x),\quad 0<x<1 NEWLINE\]NEWLINE subject to NEWLINE\[NEWLINE y(0)=0;\quad y(1)=\int_0^1k(x)y(x)dx, NEWLINE\]NEWLINE where \(q\in L^1\) and \(k\in C^2\). The authors give a detailed description of eigenvalue properties including structure and asymptotic expansion with respect to a Riesz basis. The results extends those known for the \(m\)-point one-sided boundary condition and of course the Sturm-Liouville boundary value problem.