... ProblemsVolume 2010, Article ID 690342, 21 pagesdoi:10.1155/2010/690342 Research Article Extremal Values of Half-Eigenvalues for p-Laplacian with Weights in L1BallsPing YanDepartment of Mathematical ... 0.2.23Proof. Compared with results in 8, we need only proveΣ2m1a, b∈λL2m1a, b,λR2m1a, b∀m ∈ Z. 2.24The proof of this is similar to the proof of some ... continuous in α ∈ 1, ∞. Explicit formula of Kα, p canbe found in 17, Theorem 4.1. For instance, Kp, pπppand K∞,p2p.Theorem 4.9. For any r>0, 1.11 holds for γ 1, that is,HFm,1r...