We have established multiplicity of nontrivial solutions for the quasilinear elliptic problem
−Δpu=h(x)uα−1+g(x,u)in Ω−Δpu=h(x)uα−1+g(x,u)in Ω
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u≥0in Ω,u≥0in Ω,
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u=0on ∂Ω,u=0on ∂Ω,
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where Ω⊂RNΩ⊂RN is a smooth bounded domain, p>1p>1, 1≤α