TITLE:
Positive Solution for a Singular Fourth-Order Differential System
AUTHORS:
B. Kovács
KEYWORDS:
Positive Solutions, Fixed Point Theorem, Singular Solutions, Bending of an Elastic Beam, Cone, Boundary Value Problem, Existence, Multiplicity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.9,
September
15,
2021
ABSTRACT: In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system u(4) = φu + f (t, u, u”, φ), 0 t φ” = μg (t, u, u”), 0 t u (0) = u (1) = u”(0) = u”(1) = 0, φ (0) = φ (1) = 0; where μ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.