@article {FELTRIN20174255,
	title = {Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree},
	journal = {Journal of Differential Equations},
	volume = {262},
	number = {8},
	year = {2017},
	pages = {4255 - 4291},
	abstract = {<p>We study the periodic boundary value problem associated with the second order nonlinear differential equationu"+cu'+(a+(t)-μa-(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ\&gt;0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill{\textquoteright}s equation. We prove the existence of 2m-1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin{\textquoteright}s coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.</p>},
	keywords = {Coincidence degree, Multiplicity results, Neumann boundary value problems, Positive periodic solutions, subharmonic solutions, Superlinear indefinite problems},
	issn = {0022-0396},
	doi = {https://doi.org/10.1016/j.jde.2017.01.009},
	url = {http://www.sciencedirect.com/science/article/pii/S0022039617300219},
	author = {Guglielmo Feltrin and Fabio Zanolin}
}
