Unbounded Solutions and Periodic Solutions for Second Order Differential Equations with Asymmetric Nonlinearity

@inproceedings{Xiong2007UnboundedSA,
  title={Unbounded Solutions and Periodic Solutions for Second Order Differential Equations with Asymmetric Nonlinearity},
  author={Li Xiong and Ziheng Zhang},
  year={2007}
}
In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator ẍ + f(ẋ) + ax − bx− = φ(t, x), where a and b are positive constants satisfying the nonresonant condition 1 √ a + 1 √ b / ∈ Q and φ(t, x) is 2π−periodic in the first variable and bounded.