Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (1): 1-9.doi: 10.3969/j.issn.1000-5641.2022.01.001

• Mathematics •     Next Articles

Stability of the solution to a singularly perturbed semilinear second-order differential equation with discontinuous right-hand side

Aleksei LIUBAVIN(), Mingkang NI*()   

  1. 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
  • Received:2021-01-18 Online:2022-01-25 Published:2022-01-18
  • Contact: Mingkang NI E-mail:la1992@mail.ru;xiaovikdo@163.com

Abstract:

In this paper, a stationary problem for the reaction-diffusion equation with a discontinuous right-hand side is considered. Based on ideas from contrast structure theory, the asymptotic representations for eigenvalues and eigenfunctions are constructed by solving a Sturm-Liouville problem and an estimation of the remainder is obtained. Moreover, a sufficient condition which guarantees the stability of the solution to this task is established.

Key words: singular perturbations, asymptotic approximations, stability, reaction-diffusion equation

CLC Number: