# Semilinear

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${\displaystyle Lu=F(u)}$
${\displaystyle Lu=F(u,Du,\ldots ,D^{k}u)}$
where L is a linear operator, F is a nonlinear function of the first few derivatives ${\displaystyle u,Du,\ldots ,D^{k}u}$, with k strictly less than the order of L. Semilinear-with-derivatives equations are more nonlinear than semilinear equations, but are less nonlinear than quasilinear or fully nonlinear equations.