Existence and multiplicity of solutions for an anisotropic elliptic problem involving variable exponent growth conditions

We study a boundary value problem of the type in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in (N≥ 3) with smooth boundary and the functions are of the type with , (i = 1, …, N). Combining the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle we show that under suitable conditions the problem has two non-trivial weak solutions.