We present some results which show the rich and complicated structure of the solutions of the second order differential equation x'' + w(t)g(x) = 0 when the weight w(t) changes sign and g is sufficiently far from the linear case. New applications, motivated by recent studies on the superlinear Hill’s equation in [57, 58, 59], are then proposed for some asymptotically linear equations and for some sublinear equations with a sign-indefinite weight. Our results are based on a fixed point theorem for maps which satisfy a stretching condition along the paths on two-dimensional cells.
Papini, D., Zanolin, F. (2004). On the periodic boundary value problem and chaotic-like dynamics for nonlinear Hill's equations. ADVANCED NONLINEAR STUDIES, 4(1), 71-91.
On the periodic boundary value problem and chaotic-like dynamics for nonlinear Hill's equations
PAPINI, DUCCIO;
2004-01-01
Abstract
We present some results which show the rich and complicated structure of the solutions of the second order differential equation x'' + w(t)g(x) = 0 when the weight w(t) changes sign and g is sufficiently far from the linear case. New applications, motivated by recent studies on the superlinear Hill’s equation in [57, 58, 59], are then proposed for some asymptotically linear equations and for some sublinear equations with a sign-indefinite weight. Our results are based on a fixed point theorem for maps which satisfy a stretching condition along the paths on two-dimensional cells.
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https://hdl.handle.net/11365/24316
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