The unique periodic solution of Abel's differential equation
Consider the scalar differential equation \[ \frac{{dx}}{{dt}} = a(t) x^3 + b(t) x^2 + c(t) x+ d(t) \tag{1} \] under the assumption that \(a,b,c,d\) are continuous \(\omega\)-periodic functions. The authors prove that under the additional conditions (\(i\)). \( a(t) <0 \quad (a(t)>0)\) (\(ii\)). \(b^2(t)-3a(t)<0\) equation (1) has a unique \(\omega\)-periodic solution which is asymptotically stable (unstable).
scientific article; zbMATH DE number 7221162
scientific article