Abstract
In this paper, we study the existence and multiplicity of solutions of the following quasilinear elliptic problem { − div ( a ( | ∇ u | ) ∇ u ) = f ( x , u ) , in Ω , u = 0 , on ∂ Ω , where Ω ⊂ R N is a bounded domain with smooth boundary ∂ Ω. The existence and multiplicity of solutions are obtained by genus theory, symmetric mountain pass lemma, fountain theorem and dual fountain theorem, respectively.
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