LOCALLY EKELAND＇S VARIATIONAL PRINCIPLE AND SOME SURJECTIVE MAPPING THEOREMS

This paper shows that if a Gateaux differentiable fuactional f has a finite lower bound (although it need not attain it), then, for every ε > O, there exists some point zε suchthat ||f‘(zε)|| ≤ ε / 1+h(||xε||), where h : [0, ∞) → [0,∞) is a continuous function such that ∫0^∞ 1 /1+h(γ)dγ = ∞. Applications are given to extremum problem and some surjective mappings.