# Integrability and solvability of polynomial Li\'{e}nard differential systems

@inproceedings{Demina2021IntegrabilityAS, title={Integrability and solvability of polynomial Li\'\{e\}nard differential systems}, author={Maria V. Demina}, year={2021} }

We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard differential systems describing nonlinear oscillators with a polynomial damping and a polynomial restoring force. We prove that Liénard differential systems are not Darboux integrable excluding subfamilies with certain restrictions on the degrees of polynomials arising in the systems. It is demonstrated that if the degree of a polynomial responsible for the restoring force is higher than the degree of a…

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