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.