Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (2): 26-33.doi: 10.3969/j.issn.1000-5641.2023.02.005

• Mathematics • Previous Articles     Next Articles

A class of second-order semilinear singularly perturbed boundary value problems with turning points

Min ZHAO, Mingkang NI*()   

  1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
  • Received:2021-04-21 Online:2023-03-25 Published:2023-03-23
  • Contact: Mingkang NI


The dynamical behavior of a class of second-order semilinear singularly perturbed Neumann boundary value problems with a turning point are studied. Firstly, we establish sufficient conditions for the exchange of stabilities near the turning point. By correcting the regularized equation of the degenerate problem, the accuracy of the asymptotic solution to the original problem is improved. Secondly, the Nagumo theorem is used to prove the existence of a smooth solution. Finally, a specific example is used to verify the validity of the results.

Key words: singular perturbation, boundary value problems, turning point, exchange of stabilities, asymptotic solution

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