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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 5

Issues

Remarks on a semilinear system in ℝn motivated by difference equations

Diogo Caetano / Luís Sanchez
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0169

Abstract

We study some conditions of solvability of a semilinear system in ℝn, where the linear part is represented by an n × n matrix with one-dimensional kernel and the nonlinear term is a sublinear, continuous vector field.

MSC 2010: 39A11

Keywords: difference equations; resonance; sign condition; Landesman-Lazer condition

This work was supported by Fundação Calouste Gulbenkian, Programme Novos Talentos em Matemática 2014 (Diogo Caetano) and by Fundação para a Ciência e a Tecnologia, UID/MAT/04561/2013 (Luís Sanchez)

References

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    DRÁBEK, P.—LANGERO, M.: Landesman-Lazer condition revisited: the influence of vanishing and oscillating nonlinearities, Electron. J. Qual. Theory Differ. Equ. 68 (2015), 1–11.Google Scholar

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    LANDESMAN, E. M.—LAZER, A. C.: Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609–623.Google Scholar

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    MA, R.: Nonlinear discrete Sturm-Liouville problems at resonance, Nonlinear Anal. 67 (2007), 3050–3057.Google Scholar

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    RODRIGUEZ, J.: Nonlinear discrete Sturm-Liouville problems, J. Math. Anal. Appl. 308 (2007), 380–391.Google Scholar

About the article

Received: 2016-09-16

Accepted: 2017-11-23

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Michal Fečkan


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1075–1082, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0169.

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