Abstract
It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in \({\mathbb{R}^N}\) with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in \({H^1(\mathbb{R}^N)}\) 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.
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Silva, E.A.B., Vieira, G.F. Quasilinear asymptotically periodic Schrödinger equations with critical growth. Calc. Var. 39, 1–33 (2010). https://doi.org/10.1007/s00526-009-0299-1
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DOI: https://doi.org/10.1007/s00526-009-0299-1