Abstract:

Consider the equation $$x''+beta sin x=f(t)$$ where the forcing is $2pi$-periodic and satisfies $$ int_0^{2pi} f(t)dt =0.$$ I present the following result: assuming $0<beta <1/4$, for almost every forcing there exists a stable $2pi$-periodic solution. The sentence “for almost every forcing” is understood in the sense of prevalence and is needed, the result is false for some forcings. The number 1/4 is sharp.