Abstract
In this paper we study the following p ( x ) -Laplacian problem: − div ( a ( x ) | ∇ u | p ( x ) − 2 ∇ u ) + b ( x ) | u | p ( x ) − 2 u = f ( x , u ) , x ∈ Ω , u = 0 , on ∂ Ω , where 1 < p 1 ⩽ p ( x ) ⩽ p 2 < n , Ω ⊂ R n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in W 0 1 , p ( x ) ( Ω ) for the p ( x ) -Laplacian problems in the superlinear and sublinear cases.
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