Nonexistence of monotonic solutions of some third-order ODE relevant to the Kuramoto-Sivashinsky equation (Q5928411)

The authors establish that there is no monotone solution for certain range of the parameter \(\lambda\) to the third-order ordinary differential equation of the form NEWLINE\[NEWLINE\lambda y'''+ y'= f(y),\quad y= y(x),\quad x\in\mathbb{R},NEWLINE\]NEWLINE where \(\lambda\) is a parameter and \(f\) satisfies some smoothness conditions.