Abstract
In this paper, we are concerned with the following third-order ordinary differential equation: x‴(t)+f t,x(t),x′(t),x″(t) =0, 0<t<1, with the nonlinear boundary conditions x(0)=0, g x′(0),x″(0) =A, h x′(1),x″(1) =B, where A, B∈ R, f :[0,1]×R 3→R is continuous, g, h: R 2→ R are continuous. The existence result is given by using a priori estimate, Nagumo condition, upper and lower solutions and Leray–Schauder degree, and we give an example to demonstrate our result.
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