Abstract
In this paper, we establish the Nagumo theorems for boundary value problems associated with a class of third-order singular nonlinear equations: $(p(t)x')''=f(t,x,p(t)x',(p(t)x')')$ , $\forall t\in(0,1)$ by the method of upper and lower solutions and the Schauder fixed point theorem. We also consider the multiplicity of the solutions by using topological degree theory. There are some examples to illustrate how the results of this paper can be applied.
Highlights
The singular differential equations arise in the fields of fluid mechanics, gas dynamics and so on
The method of upper and lower solutions has become a standard tool in studying the solvability of boundary value problems associated with the differential equations [ – ]
For two-point BVPs, Yao and Feng employed the upper and lower solution method to prove the existence of solutions for a kind of third-order nonlinear differential equations [ ]
Summary
The singular differential equations arise in the fields of fluid mechanics, gas dynamics and so on. The method of upper and lower solutions has become a standard tool in studying the solvability of boundary value problems associated with the differential equations [ – ]. The existence of a solution for the boundary value problem y = g x, y, y , y , x ∈ (a, c), y(a) = α, y (a) = α , y (c) = γ , a < c, is investigated in article [ ].
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