Differential and Integral Equations

Periodic solutions and asymptotic behavior in Liénard systems with p-Laplacian operators

M. García-Huidobro, R. Manásevich, and J.R. Ward

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We first prove the existence of periodic solutions to systems of the form \[ (\phi_{p}(u^{\prime}))^{\prime}+\frac{d}{dt}(\nabla F(u))+\nabla G(u)=e(t). \] We then study the asymptotic behavior of all solutions to such systems, and give sufficient conditions for uniform ultimate boundedness of solutions.

Article information

Differential Integral Equations, Volume 22, Number 9/10 (2009), 979-998.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J92: Quasilinear elliptic equations with p-Laplacian
Secondary: 34C11: Growth, boundedness 34C25: Periodic solutions 35B10: Periodic solutions 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]


García-Huidobro, M.; Manásevich, R.; Ward, J.R. Periodic solutions and asymptotic behavior in Liénard systems with p-Laplacian operators. Differential Integral Equations 22 (2009), no. 9/10, 979--998. https://projecteuclid.org/euclid.die/1356019518

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