It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in R N with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in H 1 (R N ) and satisfy the geometric hypotheses of the Mountain Pass Theorem. The Concentration-Compactness Principle and a comparison argument allow to verify that the problem possesses a nontrivial solution.
The main results of this paper establish, via the variational method, the multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents under the presence of symmetry. The concentration-compactness principle allows to prove that the Palais-Smale condition is satisfied below a certain level.
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