@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}
}
@article {1078-0947_2013_1_89,
	title = {Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions},
	journal = {Discrete \& Continuous Dynamical Systems - A},
	volume = {33},
	number = {1078-0947_2013_1_8},
	year = {2013},
	pages = {89},
	abstract = {<p>We study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.</p>},
	keywords = {lower and upper solutions, parameter dependent equations, Periodic solutions, Poincar{\'e}-Birkhoff twist theorem, subharmonic solutions},
	issn = {1078-0947},
	doi = {10.3934/dcds.2013.33.89},
	url = {http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f},
	author = {Alberto Boscaggin and Fabio Zanolin}
}
