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| LOCALLY EKELAND'S VARIATIONAL PRINCIPLE AND SOME SURJECTIVE MAPPING THEOREMS |
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Citation： |
Zhong Chengkui,Zhao Peihao.LOCALLY EKELAND'S VARIATIONAL PRINCIPLE AND SOME SURJECTIVE MAPPING THEOREMS[J].Chinese Annals of Mathematics B,1998,19(3):273~280 |
| Page view： 1034
Net amount： 910 |
Authors： |
Zhong Chengkui; Zhao Peihao |
Foundation： |
Project supported by the National Natural Science
Foundation of China and the Chinese University Doctoral Foundation. |
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| Abstract： |
This paper shows that if a Gateaux differentiable
functional $f$ has a finite lower bound (although
it need not attain it), then, for every $\varepsilon >0$, there exists
some point $z_\varepsilon$ such that $\|f^\prime (z_\varepsilon) \|\leq\frac{\varepsilon}{1+h(\|z_\varepsilon\|)}$,
where $h:[0,\infty)\rightarrow [0,\infty)$ is a continuous function such that
$\int_0^\infty \frac{1}{1+h(r)}dr =\infty$. Applications are given
to extremum problem and some
surjective mappings. |
Keywords： |
Variational principle, Extremum problem, Weak P.S. condition,Surjective mapping |
Classification： |
47H09, 49J45, 58E05 |
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