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Existence of a periodic solution for continuous and discrete periodic second-order equations with variable potentials

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Abstract

Green’s functions for new second-order periodic differential and difference equations with variable potentials are found, then used as kernels in integral operators to guarantee the existence of a positive periodic solution to continuous and discrete second-order periodic boundary value problems with periodic coefficient functions. A new version of the Leggett-Williams fixed point theorem is employed.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Concordia College, Moorhead, MN, 56562, USA

    Douglas R. Anderson

  2. College of Arts and Sciences, Dakota State University, Madison, SD, 57042, USA

    Richard I. Avery

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  1. Douglas R. Anderson
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  2. Richard I. Avery
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Correspondence to Douglas R. Anderson.

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Anderson, D.R., Avery, R.I. Existence of a periodic solution for continuous and discrete periodic second-order equations with variable potentials. J. Appl. Math. Comput. 37, 297–312 (2011). https://doi.org/10.1007/s12190-010-0435-2

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  • DOI: https://doi.org/10.1007/s12190-010-0435-2

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