Almost periodic solutions for an asymmetric oscillation

作者：Huang, Peng; Li, Xiong^*; Liu, Bin

来源：Journal of Differential Equations, 2017, 263(12): 8916-8946.

DOI：10.1016/j.jde.2017.08.063

• Almost periodic mappings
• Invariant curve theorem
• Asymmetric oscillations
• Almost periodic solutions
• Boundedness

In this paper we study the dynamical behavior of the differential equation
x ''+ax(+) -bx(-) = f(t),
where x(+) = max{x, 0}, x(-) = max{x, 0}, a and b are two different positive constants, f(t) is a real analytic almost periodic function. For this purpose, firstly, we have to establish some variants of the invariant curve theorem of planar almost periodic mappings, which was proved recently by the authors (see [11]). Then we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the above asymmetric oscillation.

• 出版日期2017-12-15
• 单位北京师范大学; 北京大学