Third-order nonlinear singularly perturbed boundary value problem
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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 wordsthird order boundary value problem upper and lower solutions Volterra type integral operator existence and asymptotic estimates
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- ZHAO Wei-li. Singularly perturbed of boundary value problems for third nonlinear ordinary differential equation[J].Acta Math Sci, 1988,8(1): 95–108.Google Scholar
- WANG Guo-can. Asymptotic estimation of Robin boundary value problem for third nonlinear equation[J].Soochow Journal of Mathematics, 1997,23(1): 73–80.Google Scholar
- ZHOU Qui-de. Singular perturbations for Voterra type integrodifferential equation[J].Appl Math J Chinese Univ, 1988,3(3): 392–400. (in Chinese)Google Scholar
- ZHANG Xiang. Singular perturbations for a third-order boundary value problem[J].J Anhui Normal Univ Nat Sci, 1995,18(1): 15. (in Chinese)Google Scholar