A comparison theorem for super- and subsolutions of ${\nabla }^2\mathbf{u}+\mathbf{f}(\mathbf{u})=0$ and its application to water waves with vorticity

Vladimir Kozlov, Nikolay Kuznetsov

A comparison theorem is proved for a pair of solutions that satisfy in a weak sense opposite differential inequalities with nonlinearity of the form $f(u)$ with $f$ belonging to t…