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Three solutions for a nonlinear Neumann boundary value problem

Najib Tsouli, Omar Chakrone, Omar Darhouche, Mostafa Rahmani (2014)

Applicationes Mathematicae

The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form - Δ p ( x ) u + a ( x ) | u | p ( x ) - 2 u = μ g ( x , u ) in Ω, | u | p ( x ) - 2 u / ν = λ f ( x , u ) on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.

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