# Semilinear

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A **semilinear** equation is a PDE of the form

where *L* is a linear operator and *F* is a nonlinear operator which does not involve any derivatives of *u*.

A **semilinear-with-derivatives** equation is a PDE of the form

where *L* is a linear operator, *F* is a nonlinear function of the first few derivatives , 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.