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A $p$-Laplacian elliptic problem in the presence of both strongly singularand $(p-1)$-superlinear nonlinearities is considered. We employ bifurcationtheory, approximation techniques and sub-supersolution method to establish theexistence of an unbounded branch of positive solutions, which is bounded inpositive $\lambda-$direction and bifurcates from infinity at $\lambda=0$. Asconsequence of the bifurcation result, we determine intervals of existence,nonexistence and, in particular cases, global multiplicity.

Multiplicity for a strongly singular quasilinear problem via bifurcation theory