On the structure of unbounded positive solutions to the quasilinear logistic equation

For the quasilinear logistic equation −△pu=λm(x)uα−uβ−△pu=λm(x)uα−uβ in ΩΩ, u=0u=0 on ∂Ω∂Ω with α≤p−1α≤p−1, α<βα<β, m(x)∈Lq(Ω)m(x)∈Lq(Ω), we obtain the existence of the maximal unbounded positive solutions, their asymptotic behavior and global bifurcation from the trivial solution.