The generalized solutions of a certain n order differential equations with polynomial coefficients

© 2015 Taylor & Francis. In this paper, we propose the generalized solutions of the differential equation (Formula presented.) where m and n are any integers with (Formula presented.) , and (Formula presented.) using Laplace transform technique. We find that the types of Laplace transformable...

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Main Authors: K. Nonlaopon, S. Orankitjaroen, A. Kananthai
格式: 雜誌
出版: 2018
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在線閱讀:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84941207141&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/44802
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機構: Chiang Mai University
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總結:© 2015 Taylor & Francis. In this paper, we propose the generalized solutions of the differential equation (Formula presented.) where m and n are any integers with (Formula presented.) , and (Formula presented.) using Laplace transform technique. We find that the types of Laplace transformable solutions in the space of right-sided distributions depend on the relationship between m and n. Precisely, we have a distributional solution provided (Formula presented.) , and a weak solution otherwise. Our work improves the result of Kananthai [The distribution solutions of ordinary differential equation with polynomial coefficients. Southeast Asian Bull Math. 2001;25:129–134].