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Quasilinear asymptotically periodic Schrödinger equations with critical growth

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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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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Brasília, 70910-900, Brasilia, DF, Brasil

    Elves A. B. Silva

  2. Unidade Acadêmica de Ciências Exatas e da Natureza, Centro de Formação de Professores, Universidade Federal de Campina Grande, 58900-000, Cajazeiras, PB, Brasil

    Gilberto F. Vieira

Authors
  1. Elves A. B. Silva
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  2. Gilberto F. Vieira
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Correspondence to Elves A. B. Silva.

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Communicated by P.Rabinowitz.

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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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