Existence Results for a 2nth-Order Differential Equation with Sturm-Liouville Operator. (18th August 2021)

• Record Type: Journal Article
• Authors: Heidarkhani, Shapour; Moradi, Shahin
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 11(2021)
• Page Start: 1239
• Page End: 1262
• Publication Date: 2021-08-18
• Subjects: 2nth-order differential equation -- one solution -- infinitely many solutions -- Sturm-Liouville operator -- variational methods; 34B15 -- 35A15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1954017
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Critical point results for a 2nth-order differential equation with Sturm-liouville operator is exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behavior of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behavior of the potential of the nonlinear term at infinity. Some recent results are extended and improved. Some examples are included to dwell upon the usefulness of the results obtained.