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a version of zhong's coercivity result for a general class of ...

a version of zhong's coercivity result for a general class of ...

606 A

606 A version of Zhong’s coercivity resultCorresponding to ɛ > 0, the definition of the integral yields a partition r = r N

D. Motreanu et al. 607Dividing by t>0 and then passing to the upper limit as t → 0 + ,weobtainthat1 ( (limsup Φ w0 + t ( )) ( )) ( )w − w 0 − Φ w0 + Ψ(w) − Ψ w0t→0 t + ɛ≥−1+h (∥∥ ∥) ∥∥ ∥w 0 w − w 0 .(3.14)We deduce thatΦ 0( ) ( ) ɛw 0 ;w − w 0 + Ψ(w) − Ψ w0 ≥−1+h (∥∥ ∥) ∥∥ ∥w 0 w − w 0 , ∀w ∈ X.(3.15)Since w 0 ∈ M 0 , it is known that ‖w 0 ‖≥r 0 = r ∗ ≥ 1/ɛ. From(3.8) and(3.9) weinfer that α − ɛ 2 ≤ I(w 0 )

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