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Third-order nonlinear singularly perturbed boundary value problem

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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.

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Authors and Affiliations

  1. Department of Basic Science and Engineering, Dalian Railway Institute, 116028, Dalian, P R China

    Wang Guo-can & Jin Li

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  1. Wang Guo-can
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  2. Jin Li
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Communicated by XU Zheng-fan

Biography: WANG Guo-can (1963-), Professor

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Guo-can, W., Li, J. Third-order nonlinear singularly perturbed boundary value problem. Appl Math Mech 23, 670–677 (2002). https://doi.org/10.1007/BF02437651

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  • DOI: https://doi.org/10.1007/BF02437651

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