We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation u'' + c u' + λ a(t) g(u) = 0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt<0 and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.
Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case
Alberto Boscaggin;FELTRIN, GUGLIELMO;Fabio Zanolin
2016-01-01
Abstract
We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation u'' + c u' + λ a(t) g(u) = 0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt<0 and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.
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