Canard solution and its asymptotic approximation in a second-order nonlinear singularly perturbed boundary value problem with a turning point

•We get existence of canards in a nonlinear singularly perturbed turning point problem.•We give uniformly valid zeroth-order asymptotic approximation to the canard solution.•We give error estimate between the asymptotic approximation and the canard solution.

This paper considers the existence and uniformly valid asymptotic approximation of canard solutions in a second-order nonlinear singularly perturbed boundary value problem with a turning point. We get the main results by constructing the asymptotic solution first and then defining a couple of upper and lower solutions suitably on the basis of the asymptotic solution. Two examples are carried out to illustrate and verify the theoretical results.