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.
Highlights
It is well known that the bending of an elastic beam can be described with fourth-order boundary value problems
Second-order differential system by using the fixed point theorem of cone expansion and compression
In [16], the authors use a mixed monotone operator method to investigate the existence of positive solution to a fourth-order boundary value problem which describes the deflection of an elastic beam
Summary
Journal of Applied Ma- In this paper, we investigate the existence of positive solutions for the singuthematics and Physics, 9, 2244-2257. = −φ′′ μ g (t,u,u′′), 0 < t < 1, u= (0) u= (1) u′′= (0) u′′= (1) 0, Received: June 21, 2021 Accepted: September 12, 2021 φ= (0) φ= (1) 0; where μ > 0 is a constant, and the nonlinear terms f , g. Published: September 15, 2021 may be singular with respect to both the time and space variables. Obtained generalize and improve some known results including singular and non-singular cases.
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