Abstract
In this paper, we discuss the solutions of the following p ( x ) -Laplacian problem: − div ( | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u = f ( x , u ) x ∈ R N where 1 < p − ≤ p ( x ) ≤ p + < N . Based on the theory of the variable exponent Sobolev spaces W 1 , p ( x ) ( R N ) , we get that there exist at least two non-trivial weak solutions.
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