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Multiplicity results for a class of quasilinear equations with exponential critical growth

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  • Claudianor O. Alves
  • Luciana R. de Freitas

Abstract

In this work, we prove the existence and multiplicity of positive solutions for the following class of quasilinear elliptic equations: −εNΔNu+1+μA(x)uN−2u=f(u)inRN,u>0inRN,where ΔN is the N†Laplacian operator, N≥2, f is a function with exponential critical growth, μ and ε are positive parameters and A is a nonnegative continuous function verifying some hypotheses. To obtain our results, we combine variational arguments and Lusternik–Schnirelman category theory.

Suggested Citation

  • Claudianor O. Alves & Luciana R. de Freitas, 2018. "Multiplicity results for a class of quasilinear equations with exponential critical growth," Mathematische Nachrichten, Wiley Blackwell, vol. 291(2-3), pages 222-244, February.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:2-3:p:222-244
    DOI: 10.1002/mana.201500371
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