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Revista Matemática Complutense

, Volume 32, Issue 1, pp 1–18 | Cite as

Existence of positive solutions for a class of quasilinear elliptic problems with exponential growth via the Nehari manifold method

  • Giovany M. FigueiredoEmail author
  • Fernando Bruno M. Nunes
Article
  • 106 Downloads

Abstract

In this paper we will be concerned with the problem
$$\begin{aligned} -\,\text{ div }(a(|\nabla u|^{p})|\nabla u|^{p-2}\nabla u)= f(u) \ \text{ in } \ \Omega , \ \ u=0 \ \text{ on } \ \ \partial \Omega , \end{aligned}$$
where \(\Omega \subset \mathbb {R}^{N}\) is bounded, \(1{<}p{<}N\), \(f:\mathbb {R}\rightarrow \mathbb {R}\) is a superlinear continuous function with exponential subcritical or exponential critical growth and the function a is \(C^{1}\). We use as a main tool the Nehari manifold method and our results include a large class of problems.

Keywords

p-N Laplacian Critical exponential growth Trudinger-Moser inequality 

Mathematics Subject Classification

Primary 35J60 Secondary 35C20 35B33 49J45 

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Copyright information

© Universidad Complutense de Madrid 2018

Authors and Affiliations

  • Giovany M. Figueiredo
    • 1
    Email author
  • Fernando Bruno M. Nunes
    • 2
  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasíliaBrazil
  2. 2.Departamento de Engenharia AmbientalUniversidade Estadual do Amapá - UEAPMacapáBrazil

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