Abstract
We show the existence and stability of solutions for a family of Dirichlet problems − div ( V z 1 ( x , ∇ u ) , … , V z N ( x , ∇ u ) ) + L u ( x , u ) = F u k ( x , u ) , u ∈ W 0 1 , p ( x ) ( Ω ) in a bounded domain and with nonconvex nonlinearity satisfying some local growth conditions. The conditions upon V and L allow for considering the p ( x ) -Laplacian equation. We use the relations between critical points and critical values to the primal and a suitable dual action functional to get the existence, stability and some properties of the solutions.
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