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Authors: .
is a bounded domain with smooth boundary and 
- Laplace type operator. Relying on the critical point theory and using the mountain-pass theorem, we prove the existence of a unique nontrivial weak solution for our problem. Key words and phrases. anisotropic variable exponent Sobolev spaces, quasilinear elliptic equations, critical point theory, weak solutions, existence, uniqueness, mountain-pass theorem.
