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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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