= Nonlinear coercive operator
{title2=$\langle A(u),u-u_0\rangle/\|u-u_0\|\to+\infty$}
For a map $A:M\to X^*$ on a subset of a real <Banach space>, coercivity with respect to $u_0\in M$ means the displayed limit as $u\in M$ and $\|u-u_0\|\to\infty$. Here the brackets denote the <dual pairing>. This growth condition is useful in existence theorems for <monotone operators>. A linear Hilbert-space estimate $\langle Au,u\rangle\geq c\|u\|^2$, $c>0$, implies the condition at zero. Monotonicity alone does not: the zero operator is monotone and fails this growth condition on an unbounded space.
Back to article page
