Boundary Value Problems for Liénard-Type Equations with Quadratic Dependence on the “Velocityâ€

A. Kirichuka, F. Sadyrbaev and Paul Eloe

Abstract and Applied Analysis, 2022, vol. 2022, 1-12

Abstract: The estimates were obtained for the number of solutions for the Neumann and Dirichlet boundary value problems associated with the Liénard equation with a quadratic dependence on the “velocity.†Sabatini’s transformation is used to reduce this equation to a conservative one, which does not contain the derivative of an unknown function. Despite the one-to-one correspondence between the equilibria, the topological structure of the phase portraits of both equations can differ significantly.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:9228511

DOI: 10.1155/2022/9228511

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