Existence of solutions for a class of $p(x)$-Laplacian equations involving a concave-convex nonlinearity with critical growth in $\mathbb{R}^{N}$

Authors

  • Claudianor Oliveira Alves
  • Marcelo C. Ferreira

DOI:

https://doi.org/10.12775/TMNA.2015.020

Keywords

Variational Methods, $p(x)$-Laplacian, critical growth

Abstract

We prove the existence of solutions for a class of quasilinear problems involving variable exponents and with nonlinearity having critical growth. The main tool used is the variational method, more precisely, Ekeland's Variational Principle and the Mountain Pass Theorem.
Vol 45, No 2 (June 2015)

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Published

2015-06-01

How to Cite

1.
ALVES, Claudianor Oliveira and FERREIRA, Marcelo C. Existence of solutions for a class of $p(x)$-Laplacian equations involving a concave-convex nonlinearity with critical growth in $\mathbb{R}^{N}$. Topological Methods in Nonlinear Analysis. Online. 1 June 2015. Vol. 45, no. 2, pp. 399 - 422. [Accessed 10 December 2024]. DOI 10.12775/TMNA.2015.020.

Issue

Vol 45, No 2 (June 2015)

Section

Articles

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