... CorporationBoundary Value ProblemsVolume 2009, Article ID 316812, 17 pagesdoi:10.1155/2009/316812 Research Article Variational Method to the Impulsive Equation with Neumann Boundary ConditionsJuntao ... there exists an δ>0 such that for every u with |u| <δ,Gt, u≤ ε|u|2,u0Iksds ≤ ε|u|2.3.5Hence, for any u ∈ Y with uX≤ δ/M1,by2.8 and 3.5 , we haveϕu12u2X−p−1k1e−Ltkutk0Iksds ... X.LetBrbe the open ball in X with theradius r and centered at 0 and ∂Brdenote its boundary.Theorem 2.1 22, Theorem 38.A. For the functional F : M ⊆ X → −∞, ∞ with M/ ∅, minu∈MFuα...