PreprintarXiv licencearXiv
Multiple non-collision periodic solutions for second order singular differential systems with parameters
Abstract
In this paper, new existence and multiplicity results for positive periodic solutions of singular second-order problems under sublinear and superlinear growth assumptions at infinity are established. Two aspects of our results should be highlighted in comparison with the existing literature. On the one hand, they allow for the consideration of systems exhibiting mixed behavior: sublinear in one component and superlinear in another. On the other hand, in the superlinear case, the existence of up to four positive solutions is established, whereas only two were obtained in previous works. Our approach is based on a recently established vectorial version of the Krasnoselskii-Guo fixed point theorem in product spaces.
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BibTeX
@misc{fernandezpardo2026multiple,
title = {{Multiple non-collision periodic solutions for second order singular differential systems with parameters}},
author = {Laura María Fernández-Pardo and Jorge Rodríguez-López},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14910},
eprint = {2610.14910},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14910},
}
RIS
TY - UNPB
TI - Multiple non-collision periodic solutions for second order singular differential systems with parameters
AU - Laura María Fernández-Pardo
AU - Jorge Rodríguez-López
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14910
UR - https://arxiv.org/abs/2610.14910
AB - In this paper, new existence and multiplicity results for positive periodic solutions of singular second-order problems under sublinear and superlinear growth assumptions at infinity are established. Two aspects of our results should be highlighted in comparison with the existing literature. On the one hand, they allow for the consideration of systems exhibiting mixed behavior: sublinear in one component and superlinear in another. On the other hand, in the superlinear case, the existence of up to four positive solutions is established, whereas only two were obtained in previous works. Our approach is based on a recently established vectorial version of the Krasnoselskii-Guo fixed point theorem in product spaces.
ER -