PreprintarXiv licencearXiv
Multiple solutions of singular periodic problems
Abstract
In this contribution we consider the singular periodic problem u''+k u=g(u)+e(t), u(0)=u(2π), u'(0)=u'(2π), where k∈R, e:J→R is Lebesgue integrable and g:I↦R is continuous, but can have a singularity at x=0. In particular, I wish to revisit our earlier result regarding the existence of at least two its solutions and present a proof that is somewhat more transparent than the original one.
Related
- Multiple non-collision periodic solutions for second order singular differential systems with parameters
- Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schrödinger equation
- Existence of positive solutions to singular elliptic problems with gradient terms
- Higher Regularity of Time-Periodic Solutions to Nonautonomous Hyperbolic Problems: Away from Resonances
- Entropy on regular sets and periodic-orbit growth for singular flows
BibTeX
@misc{tvrdy2026multiple,
title = {{Multiple solutions of singular periodic problems}},
author = {Milan Tvrdý},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04501},
eprint = {2610.04501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04501},
}
RIS
TY - UNPB
TI - Multiple solutions of singular periodic problems
AU - Milan Tvrdý
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04501
UR - https://arxiv.org/abs/2610.04501
AB - In this contribution we consider the singular periodic problem u''+k u=g(u)+e(t), u(0)=u(2π), u'(0)=u'(2π), where k∈R, e:J→R is Lebesgue integrable and g:I↦R is continuous, but can have a singularity at x=0. In particular, I wish to revisit our earlier result regarding the existence of at least two its solutions and present a proof that is somewhat more transparent than the original one.
ER -