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On lower and upper solutions without ordering on time scales

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In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ordering. We use the degree theory and a priori estimates to obtain the existence of solutions for the second-order Dirichlet boundary value problems. To illustrate a wider application of this result, we conclude with an example which shows that a combination of well and non-well ordered pairs can yield the existence of multiple solutions.



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Correspondence to Petr Stehlík.

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Stehlík, P. On lower and upper solutions without ordering on time scales. Adv Differ Equ 2006, 073860 (2006) doi:10.1155/ADE/2006/73860

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