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Multiple Positive Symmetric Solutions to -Laplacian Dynamic Equations on Time Scales

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  • You-Hui Su
  • Can-Yun Huang

Abstract

This paper makes a study on the existence of positive solution to -Laplacian dynamic equations on time scales . Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

Suggested Citation

  • You-Hui Su & Can-Yun Huang, 2009. "Multiple Positive Symmetric Solutions to -Laplacian Dynamic Equations on Time Scales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-27, December.
  • Handle: RePEc:hin:jnddns:141929
    DOI: 10.1155/2009/141929
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