Variational Estimation Methods for Sturm–Liouville Problems

Abstract

In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (the variational equation associated through the Euler–Lagrange variational principle and Nehari’s method, shooting method and bisection method) and iterative variational methods (He’s method and HPM) for regular RSL are unitary presented in final part of the paper, which ends with applications.

Variational approach to a symmetric boundary value problem generated by a system of equations and separated boundary conditions

“…However, we will introduce the results on the eigenvalues and eigenfunctions of the problem (1)-(3) using only energy and mean and they do not need absolute continuity for the functions. For some variational problems, the readers may see the works [18][19][20][21][22][23][24].…”