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• W2964165132 abstract "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>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill'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'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." @default.
• W2964165132 created "2019-07-30" @default.
• W2964165132 creator A5063421765 @default.
• W2964165132 creator A5091871773 @default.
• W2964165132 date "2017-04-01" @default.
• W2964165132 modified "2023-10-02" @default.
• W2964165132 title "Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree" @default.
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• W2964165132 doi "https://doi.org/10.1016/j.jde.2017.01.009" @default.
• W2964165132 hasPublicationYear "2017" @default.
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