Some remarks on a nonhomogeneous eigenvalue problem related to generalized trigonometric functions. (January 2020)

• Record Type: Journal Article
• Authors: Cheng, Yan-Hsiou; Wang, Wei-Chuan
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 34A55 -- 34B15 -- 34B24; p-Laplacian -- Inverse nodal problem -- Ambarzumyan problem -- Nonhomogeneous eigenvalue problem -- Basis property; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111614
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, a nonhomogeneous eigenvalue problem with p -Laplacian is studied. We first show the Sturm–Liouville property and derive the asymptotic expansion of eigenvalues and eigenfunctions. Employing the derivation of the eigenfunctions, we discuss the basis property related to the eigenfunctions. Finally, we also solve two inverse problems, the inverse nodal problem and Ambarzumyan problem.