Abstract
In this work, we investigate a class of nonlinear fourth-order systems with coupled integral boundary conditions and two parameters. We give the Green's functions for the system with boundary conditions, and then obtain some useful properties of the Green's functions. By using the Guo–Krasnosel'skii fixed-point theorem and the Green's functions, some sufficient conditions for the existence of positive solutions are presented. As applications, two examples are presented to illustrate the application of our main results.
Highlights
The purpose of this paper is to consider the existence of positive solutions for the following system of fourth-order differential equations: u(4)(t) = λf t, u(t), v(t), t ∈ [0, 1], (1)
We will establish some sufficient conditions on two parameters λ, μ and nonlinear terms f, g such that positive solutions of (1)–(2) exist
In [9], the authors studied the existence of positive solutions for systems of the fourth-order singular semipositone Sturm–Liouville boundary value problems u(i4)(t) = fi t, u1(t), u2(t), u1 (t), u2 (t), t ∈ (0, 1), αiui(0) − βiui(0) = 0, νiui(1) − δiui(1) = 0, αiui (0) − βiui (0) = 0, νiui (1) − δiui (1) = 0, i = 1, 2, where αi, νi > 0, βi, δi 0, ρi = νiβi + αiνi + αiδi > 0, fi ∈ C((0, 1) × R+ × R+ × R− × R−, R) with R = (−∞, +∞), R+ = [0, +∞), R− =
Summary
In [9], the authors studied the existence of positive solutions for systems of the fourth-order singular semipositone Sturm–Liouville boundary value problems u(i4)(t) = fi t, u1(t), u2(t), u1 (t), u2 (t) , t ∈ (0, 1), αiui(0) − βiui(0) = 0, νiui(1) − δiui(1) = 0, αiui (0) − βiui (0) = 0, νiui (1) − δiui (1) = 0, i = 1, 2, where αi, νi > 0, βi, δi 0, ρi = νiβi + αiνi + αiδi > 0, fi ∈ C((0, 1) × R+ × R+ × R− × R−, R) with R = (−∞, +∞), R+ = [0, +∞), R− =
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
