An eigenvalue result for Neumann BVPs with functional terms
Provides a theoretical and numerical framework for eigenvalue problems in a specific class of BVPs, but the contribution is incremental and domain-specific.
The paper studies eigenvalue-eigenfunction pairs for Neumann boundary value problems with functional terms, reformulating them as Hammerstein integral equations and providing a convergent fixed-point iteration scheme with MATLAB implementation. Numerical results validate theoretical localization bounds.
We study the existence and localization of eigenvalue-eigenfunction pairs for parameter-dependent Neumann BVPs with a functional term. By reformulating the problems as a Hammerstein integral equation, we apply an existence and localization result and propose a convergent fixed-point iteration scheme. Finally, two pseudocodes and a MATLAB implementation are provided to numerically approximate the eigenvalues and validate the theoretical localization bounds. We also illustrate an approximation of the eigenfunctions for a fixed norm.