Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree

@article{Feltrin2015MultiplicityOP,
  title={Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree},
  author={Guglielmo Feltrin and F. Zanolin},
  journal={arXiv: Classical Analysis and ODEs},
  year={2015}
}
We study the periodic boundary value problem associated with the second order nonlinear differential equation $$ u" + c u' + \left(a^{+}(t) - \mu \, a^{-}(t)\right) g(u) = 0, $$ where $g(u)$ has superlinear growth at zero and at infinity, $a(t)$ is a periodic sign-changing weight, $c\in\mathbb{R}$ and $\mu>0$ is a real parameter. We prove the existence of $2^{m}-1$ positive solutions when $a(t)$ has $m$ positive humps separated by $m$ negative ones (in a periodicity interval) and $\mu$ is… Expand

Figures from this paper

Positive subharmonic solutions to nonlinear ODEs with indefinite weight
Three positive solutions to an indefinite Neumann problem: a shooting method
...
1
2
...

References

SHOWING 1-10 OF 76 REFERENCES
Fixed points indices and period-doubling cascades
Multiple positive solutions for a superlinear problem: a topological approach
Continuation theorems for Ambrosetti-Prodi type periodic problems
A Seven-Positive-Solutions Theorem for a Superlinear Problem
Superlinear Indefinite Equations on the Real Line and Chaotic Dynamics
...
1
2
3
4
5
...