Journal of East China Normal University(Natural Sc ›› 2017, Vol. 2017 ›› Issue (2): 20-28.doi: 10.3969/j.issn.1000-5641.2017.02.003

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Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients

XUE Hu, XIE Feng   

  1. Department of Applied Mathematics, Donghua University, Shanghai 201620, China
  • Received:2016-01-06 Online:2017-03-25 Published:2017-03-23


The existence and asymptotic estimates of solutions for a class of singularly perturbed boundary value problems with discontinuous coefficients are investigated in this paper. Firstly, by using the Schauder fixed point theorem, a theorem of lower-upper solutions for general problems is established. Secondly, the formal asymptotic solution is constructed by the method of boundary functions, and the existence and uniform validity of the solution are proved by using the theorem of lower-upper solutions. Finally, an example is presented as an illustration.

Key words: singular perturbation, discontinuous coefficients, lower-upper solutions

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