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Several Existence Theorems of Multiple Positive Solutions of Nonlinear -Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales

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Abstract

By using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear -point boundary value problem for the following second-order boundary value problem on time scales , , , , where is an increasing homeomorphism and homomorphism and . Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems, respectively. In particular, our criteria generalize and improve some known results by Ma and Castaneda (2001). We must point out for readers that there is only the -Laplacian case for increasing homeomorphism and homomorphism. As an application, one example to demonstrate our results is given.

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Correspondence to Shugui Kang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
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