Asymptotic representation of the solution of a nonlinear system with resonance (Q793207)

Consider the nonlinear nonautonomous system \(\dot x+\alpha y^{\nu}=\epsilon f(x,y,\mu t) j-x^{1/\nu}=\epsilon g(x,y,\mu t)\) where f and g are analytical and 2\(\pi\)-periodic with respect to \(\mu\) t, \(\nu =(2m+1)/(2l+1)\), m,\(l=0,1,2,..\). and \(\epsilon>0\) is small. The solutions are written as asymptotic series under the assumption that \(\mu\approx 2\pi /T\), \(T=(2/(\nu +1))(\nu /\alpha)^{1/(\nu +1)}\Gamma(\nu /(\nu +1))\Gamma(1/(\nu +1)).\)