Using arecentmodified version of the Poincare-Birkhoff fixed point theorem [19], we study the existence of one-signed T-periodic solutions and sign-changing subharmonic solutions to the second order scalar ODE u′+f(t, u) = 0, being f: ℝ x ℝ → ℝ a continuous function T-periodic in the first variable and such that f(t, 0) = 0. Partial extensions of the results to a general planar Hamiltonian systems are given, as well.
One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations
BOSCAGGIN, Alberto
2012-01-01
Abstract
Using arecentmodified version of the Poincare-Birkhoff fixed point theorem [19], we study the existence of one-signed T-periodic solutions and sign-changing subharmonic solutions to the second order scalar ODE u′+f(t, u) = 0, being f: ℝ x ℝ → ℝ a continuous function T-periodic in the first variable and such that f(t, 0) = 0. Partial extensions of the results to a general planar Hamiltonian systems are given, as well.
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