Bifurcation for nonlinear eigenvalue p-Lapalcian problems involving L^q-norm

In this paper, we study a global bifurcation phenomenon associated with the non-linear problem -Δₚu= λ \|u\|qp-q |u|q-2u + f(x, u, λ)\;\; in\;\; Ω, (Ef) where, the unknown u∈ W₀1,p(Ω). Under some natural hypotheses on the nonlinear perturbation f, we prove that (λ₁, 0 ) is a global bifurcation point of the above problem, where λ₁ stands the first eigenvalue of (E_≡ 0\).