Existence of multiple unbounded solutions for a three-point boundary value problems on an infinite time scales

• Published in: Journal of applied analysis Vol. 31; no. 1; pp. 121 - 142
• Main Authors: Panigrahi, Saroj, Das, Sasmita
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.06.2025; Walter de Gruyter GmbH
• Subjects: 34B10; 34B40; 39A10; Applied mathematics; Boundary conditions; Boundary value problems; Calculus; Fixed points (mathematics); integral boundary conditions; Lower and upper solutions; Ordinary differential equations; Time; time scales; topological degree theory
• ISSN: 1425-6908; 1869-6082
• DOI: 10.1515/jaa-2023-0152

In this paper, we consider the second-order three point boundary value problem on time scales with integral boundary conditions on a half-line. We will use the upper and lower solution method along with the Schauder’s fixed point theorem to establish the existence of at least one solution which lies between pairs of unbounded upper and lower solutions. Further, by assuming two pairs of unbounded upper and lower solutions, the Nagumo condition on the nonlinear term involved in the first-order derivative, we will establish the existence of multiple unbounded solutions on an infinite interval by using the topological degree theory. The results of this paper extend the results of Akcan and Çetin (2018), Akcan and Hamal (2014), Eloe, Kaufmann and Tisdell (2006), and generalize the results of Lian and Geng (2011). Examples are included to illustrate the validation of the results.