Abstract:This paper is concerned with the existence of bounded or unbounded solutions to third-order boundary value problem on the half-line with functional boundary conditions. The arguments are based on the Green functions, a~Nagumo condition, Schauder fixed point theorem and lower and upper solutions method. An application to a Falkner-Skan equation with functional boundary conditions is given to illustrate our results.
Keywords: functional boundary conditions; unbounded solutions; half-line; upper and lower solutions; Nagumo condition; Green's function; fixed point theory; Falkner-Skan equation
DOI: DOI 10.14712/1213-7243.2015.220
AMS Subject Classification: 34B10 34B15 34B27 34B40 34B60 45G10