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In this paper, we deal with existence, uniqueness and exact rate of boundarybehavior of blow-up solutions for a class of logistic type quasilinear problemin a smooth bounded domain involving the $p$-Laplacian operator, where thenonlinearity can have a singular behavior. In the proof of the existence ofsolution, we have used the sub and super solution method in conjunction withvariational techniques and comparison principles. Related to the rate onboundary and uniqueness, we combine a comparison principle proved in thepresent paper together with the our result of existence of solution.

Blow-up solutions for a Blow-up solutions for a Blow-up solutions for a $p$-Laplacian elliptic equation of logistic type with singular nonlinearity