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The multiplicity and concentration of positive solutions are established for the equation −ε p Δ p u + V (z)|u| p-2 u = f(u) in IR N , where V is a positive continuous function and f ∈ C 1  is a function having subcritical and superlinear growth.

Multiplicity of Positive Solutions For a Quasilinear Problem in IR N Via Penalization Method