Applied Mathematics and Mechanics

, Volume 23, Issue 6, pp 670–677

Third-order nonlinear singularly perturbed boundary value problem

• Wang Guo-can
• Jin Li
Article

Abstract

Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.

The results shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.

Key words

third order boundary value problem upper and lower solutions Volterra type integral operator existence and asymptotic estimates

O175.8

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© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

• Wang Guo-can
• 1
• Jin Li
• 1
1. 1.Department of Basic Science and EngineeringDalian Railway InstituteDalianP R China