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

• Published in: Boundary value problems Vol. 2018; no. 1; pp. 1 - 19
• Main Authors: Lu, Shiping, Yu, Xingchen
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 28.06.2018; Hindawi Limited; SpringerOpen
• Subjects: Analysis; Approximations and Expansions; Boundary value problem; Difference and Functional Equations; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Periodic functions; Periodic solution; Singularity; Singularity (mathematics); Upper and lower functions; Singularity; Boundary value problem; Periodic solution; Upper and lower functions

In this paper, we study the periodic problem for the Liénard equation with an indefinite singularity of attractive type x ″ + f ( x ) x ′ + φ ( t ) x + r ( t ) x μ = 0 , where f : ( 0 , + ∞ ) → R is continuous and may have singularities at zero, r , φ : R → R are T -periodic functions, and μ is a po...