Parameter dependent estimates for solutions of Sturm-Liouville equation (Q2722117)

The authors obtain estimates on solutions to the equation NEWLINE\[NEWLINE y''(x)+[\mu^2\rho (x)-q(x)]y(x)=0,\quad 0\leq x\leq 1, NEWLINE\]NEWLINE for \(\mu \to \infty\). It is assumed that \(\rho\) is a strictly positive function of bounded variation, \(q\) is real-valued and integrable. In particular, uniform (with respect to \(\mu\), \(|\text{Im} \mu|\leq r<\infty\)) estimates in the norm of \(C[0,1]\) are given. As an application the location of the spectrum for the parameter dependent boundary conditions is studied.