Pairs of positive periodic solutions of nonlinear ODEs with indefinite\n weight: a topological degree approach for the super-sublinear case

2015/03/18 by Alberto Boscaggin, Boscaggin, Alberto, Guglielmo Feltrin +3
Mathematics · #Nonlinear Differential Equations Analysis #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1503.05310

Abstract

We study the periodic and the Neumann boundary value problems associated with\nthe second order nonlinear differential equation \u'' + c u' +\n
lambda a(t) g(u) = 0, where g colon\n mathopen[0,+\∞ mathclose[\→ mathopen[0,+\∞ mathclose[ is a\nsublinear function at infinity having superlinear growth at zero. We prove the\nexistence of two positive solutions when \∫₀^T a(t) !dt < 0 and\n\λ > 0 is sufficiently large. Our approach is based on Mawhin's\ncoincidence degree theory and index computations.\n

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