The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS

  • Received : 2011.11.16
  • Accepted : 2012.04.03
  • Published : 2012.05.31
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Abstract

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

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References

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