The Lazer–Solimini equation with state-dependent delay

Gutierrez, Alexander; Torres, Pedro J.

doi:10.1016/j.aml.2011.10.004

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“…In the past years, many mathematical researchers focused their attention on the equations with singularities [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. As is widely acknowledged, the paper [18] by Lazer and Solimini is a major milestone for the study of periodic problem to second-order differential equations with singularities.…”

Section: Introductionmentioning

confidence: 99%

Existence of positive periodic solutions for Liénard equations with an indefinite singularity of attractive type

2018

Bound Value Probl

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In this paper, we study the periodic problem for the Liénard equation with an indefinite singularity of attractive typewhere f : (0, +∞) → R is continuous and may have singularities at zero, r, ϕ : R → R are T-periodic functions, and μ is a positive constant. Using the method of upper and lower functions, we obtain some new results on the existence of positive periodic solutions to the equation.

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