Existence results for a Kirchhoff-type second-order differential equation on the half-line with impulses

Article type: Research Article

Authors: Heidarkhani, Shapour^{a; *} | Afrouzi, Ghasem A.^b | Moradi, Shahin^b

Affiliations: [a] Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran. E-mail: s.heidarkhani@razi.ac.ir | [b] Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. E-mails: afrouzi@umz.ac.ir, shahin.moradi86@yahoo.com

Correspondence: [*] Corresponding author. E-mail: s.heidarkhani@razi.ac.ir.

Abstract: We shall discuss the existence of at least one weak solution and infinitely many weak solutions for a Kirchhoff-type second-order impulsive differential equation on the half-line. Our technical approach is based on variational methods. Some recent results are extended and improved. Some examples are presented to demonstrate the application of our main results.

Keywords: Half-line, impulsive differential equation, Kirchhoff-type problem, one weak solution, infinitely many weak solutions, variational methods

DOI: 10.3233/ASY-171437

Journal: Asymptotic Analysis, vol. 105, no. 3-4, pp. 137-158, 2017