Extremum estimates of the $ L^1 $ -norm of weights for eigenvalue problems of vibrating string equations based on critical equations
Jiangang Qi, Bing Xie · Discrete and Continuous Dynamical Systems - B · 2020
The present paper is concerned with the extremal problem of the \begin{document}$ L^1 $\end{document} -norm of the weights for non-left-definite eigenvalue problems of vibrating string equations with separated boundary conditions. Applying the critical equations of the weights, the infimum is obtained in terms of the given eigenvalue and the parameter in boundary conditions.