Applied mathematics

The methods to solve some classes boundary value problems via the results in double controlled metric-like spaces

N. Souayah^ab, Z. D. Mitrovic<sup>c

a</sup> King Saud University, P. Box 145111, Riyadh, 4545, Saudi Arabia
^b University of Tunis, 92, Boulevard du 9 Avril 1938, Tunis, 1938-1007, Tunisia
^c University of Banja Luka, 1A, Bulevar vojvode Petra Bojovica, Banja Luka, 78000, Bosnia and Herzegovina

Abstract: In this paper, we present some methods to solve second-order and fourth-order boundary value problems. First, we start by proving some new fixed point theorems in double controlled metric-like space. Further, we introduce the notion of $G_{\zeta}$-contraction in the same space endowed with a graph and obtain a result on fixed points for $G_{\zeta}$-contraction. As an application of the obtained results, we implemented the existence of solutions for some classes of second-order and fourth-order boundary value problems.

Keywords: differential equations, fixed point, graph theory, double controlled metric-like spaces.

UDC: 517.988, 517.988.8

MSC: 54H25, 47H10

Received: May 7, 2024
Accepted: December 12, 2024

Language: English

DOI: 10.21638/spbu10.2025.105