Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Discrete resonance problems subject to periodic forcing


Authors: Stephen B. Robinson and Klaus Schmitt
Journal: Proc. Amer. Math. Soc. 148 (2020), 471-477
MSC (2010): Primary 15A24, 35P30, 39A45, 65H10
DOI: https://doi.org/10.1090/proc/14713
Published electronically: July 30, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider the following discrete nonlinear problem which is subject to a periodic nonlinear forcing term:

$\displaystyle A u = \lambda u +p(u) + h,$    

where $ A$ is an $ n\times n $ matrix with real components, $ p: \mathbb{R}^n\to \mathbb{R}^n$ is a periodic forcing term, and $ \langle h,\overline {\phi } \rangle =0$, where $ \overline {\phi }$ is an eigenvector of $ A^T,$ the transpose of $ A$, corresponding to a simple real eigenvalue $ \lambda $. Conditions on these terms will be provided such that this problem will have infinitely many distinct solutions. The results here are motivated by some recent results for discrete systems and by results obtained for analogous boundary value problems for semilinear elliptic problems at resonance.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 15A24, 35P30, 39A45, 65H10

Retrieve articles in all journals with MSC (2010): 15A24, 35P30, 39A45, 65H10


Additional Information

Stephen B. Robinson
Affiliation: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, North Carolina 27109
Email: sbr@wfu.edu

Klaus Schmitt
Affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112
Email: schmitt@math.utah.edu

DOI: https://doi.org/10.1090/proc/14713
Keywords: Discrete resonance problems, Brouwer, Leray-Schauder continuation, quasi-periodic functions
Received by editor(s): March 16, 2019
Received by editor(s) in revised form: May 17, 2019
Published electronically: July 30, 2019
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society