Quasi-bounded 擬有界

Definition

• $F:\mathbb{R}\times X\to {\mathbb{R}}^N$: cont. functional

F is quasi-bounded if it is bdd on every bounded closed subset of $\mathbb{R}\times X$.

Examples

The functional $F$ in this example is quasi-bdd. (Check this by noting that cont. ft. maps cpt. set to cpt. set)

(c.f. NTHU MATH 526500 DDE Note week 3)