Monotonicity of the period function of the Liénard equation of second kind

Abstract

This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Liénard II type equation given by $\ddot{x}+f(x){\dot{x}}^2+g(x)=0$. We generalize Chicone's result regarding the monotonicity of the period function to planar Hamiltonian vector fields in the presence of a position dependent mass. Sufficient conditions are also given for the isochronicity of the potential in case of such a system.

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