Periodic solutions to the Liénard type equations with phase attractive singularities
1 Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, Brno, 616 62, Czech Republic
2 Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva s/n, Granada, 18071, Spain
Boundary Value Problems 2013, 2013:47 doi:10.1186/1687-2770-2013-47Published: 6 March 2013
Sufficient conditions are established guaranteeing the existence of a positive ω-periodic solution to the equation
where , , δ are non-negative constants, c, μ, ν, γ are real numbers, and . The last equation also covers the so-called Rayleigh-Plesset equation, frequently used in fluid mechanics to model the bubble dynamics in liquid. In the paper, the case when , i.e., the case which covers the attractive singularity of the function g, is studied. The results obtained assure that there exists a positive ω-periodic solution to the above-mentioned equation if the power μ or ν is sufficiently large.
MSC: 34C25, 34B16, 34B18, 76N15.