Nontrivial solutions of inverse discrete problems with sign-changing nonlinearities
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Abstract
This paper is concerned with the existence of solutions of an inverse discrete problem
with sign-changing nonlinearity. This kind of problems includes, as a particular case,
nth order difference equations coupled with suitable conditions on the boundary of
the interval of definition. It would be valid for the case in which the related Green’s
function is positive on a subset of its rectangle of definition.
The existence results follow from spectral theory, as an application of the
Krein–Rutman theorem and by means of degree theory
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Bibliographic citation
Cabada, A., Dimitrov, N.D. Nontrivial solutions of inverse discrete problems with sign-changing nonlinearities. Adv Differ Equ 2019, 450 (2019). https://doi.org/10.1186/s13662-019-2383-y
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https://doi.org/10.1186/s13662-019-2383-ySponsors
First author is partially supported by Xunta de Galicia (Spain), project EM2014/032 and AIE, Spain and FEDER, grant
MTM2016-75140-P. The second author is supported by the Bulgarian National Science Foundation under Project DN 12/4
“Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and
environmental pollution”
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© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in anymedium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made