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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.19 No.2

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EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.2, pp.103-109
https://doi.org/10.7468/jksmeb.2012.19.2.103
Kim, Yong-In
Kim,, Y. (2012). EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(2), 103-109, https://doi.org/10.7468/jksmeb.2012.19.2.103

Abstract

The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: <TEX>$$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$</TEX> are investigated, where <TEX>${\phi}_p(u)={\mid}u{\mid}^{p-2}u$</TEX> with <TEX>$p$</TEX> > 1 and <TEX>${\alpha}{\in}C^1$</TEX>, <TEX>$e{\in}C$</TEX> are T-periodic and <TEX>$g$</TEX> is continuous and T-periodic in <TEX>$t$</TEX>. By using coincidence degree theory, some existence and uniqueness results are obtained.

keywords
p-Laplacian, degree theory, periodic solution

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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