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Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight

TitlePairs of positive periodic solutions of second order nonlinear equations with indefinite weight
Publication TypeJournal Article
Year of Publication2012
AuthorsBoscaggin, A, Zanolin, F
JournalJournal of Differential Equations
Volume252
Pagination2900 - 2921
ISSN0022-0396
KeywordsCritical points; Necessary conditions; Pairs of positive solutions; Periodic solutions
Abstract

We study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

URLhttp://www.sciencedirect.com/science/article/pii/S0022039611003895
DOI10.1016/j.jde.2011.09.011

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