... solution of (1.1) ifJλ(u), v =0 for allv ∈ D1,p0() and a solution of (1.1) is a critical point of Jl.Hsu Boundary Value Problems 2011, 2011:37http://www.boundaryvalueproblems.com/content/2011/1/37© ... infn→∞Jλ(un)=αλ,Hsu Boundary Value Problems 2011, 2011:37http://www.boundaryvalueproblems.com/content/2011/1/37Page 8 of 15RESEARC H Open AccessMultiple positive solutions for a class of quasi-linear ... SinceJλ(un)=o(1)as n ® ∞ and {un} is bounded inD1,p0(),thenby(5.2),wecandeducethatHsu Boundary Value Problems 2011, 2011:37http://www.boundaryvalueproblems.com/content/2011/1/37Page 9 of 15Set1=...