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We establish the existence of multi-bump solutions for the following class ofquasilinear problems $$  - \Delta_{ p(x) } u + \big( \lambda V(x) + Z(x) \big) u ^{ p(x)-1 } = f(x,u)\text{ in } \mathbb R^N, \, u \ge 0 \text{ in } \mathbb R^N, $$ where thenonlinearity $ f \colon \mathbb R^N \times \mathbb R \to \mathbb R $ is acontinuous function having a subcritical growth and potentials $ V, Z \colon\mathbb R^N \to \mathbb R $ are continuous functions verifying some hypotheses.The main tool used is the variational method.

Multi-bump solutions for a class of quasilinear problems involving variable exponents