MMN-615
Monotone positive solution of nonlinear third-order two-point boundary value problem
Abstract
In this paper, we are concerned with the existence of monotone
positive solution to the nonlinear third-order two-point boundary
value problem
$$\left\{\aligned &x'''(t)+f(x(t))=0,\quad t\in(0, 1),\\
&x(0)=x''(0)=x'(1)=0. \endaligned\right.$$ Under suitable
assumptions on $f$ and by using a fixed point theorem of cone
expansion and compression of functional type due to Avery, Anderson
and Krueger, we establish the existence of at least one positive
solution of the boundary value problem.
Vol. 15 (2014), No. 2, pp. 743-752