Small almost periodic and almost automorphic oscillations in forced Liénard equations
Résumé
We consider forced Liénard differential equations in the form x''(t) + f(x(t),p)x'(t) + g(x(t),p) = e(p,t), where p is a parameter in a Banach space. Starting from the zero solution when p=0, we prove the existence of almost periodic (respectively almost automorphic) solutions x(p,.) when e(p,.) is almost periodic (respectively almost automorphic), when p belongs to a neighborhood of 0. We also consider the equations x''(t) + f(x(t))x'(t) + g(x(t)) = e(t) and x''(t) + f(x(t),q)x'(t) + g(x(t),p) = e(t) which are special cases of the previous equations.