# Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space

@article{Alves2015MultiplicityAC,
title={Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space},
author={Claudianor Oliveira Alves and Ailton R. Silva},
journal={Journal of Mathematical Physics},
year={2015},
volume={57},
pages={111502}
}
• Published 2015
• Physics, Mathematics
• Journal of Mathematical Physics
In this work, we study existence, multiplicity, and concentration of positive solutions for the following class of quasilinear problems − Δ Φ u + V ( ϵ x ) ϕ ( u ) u = f ( u ) in R N ( N ≥ 2 ) , where Φ ( t ) = ∫ 0 t ϕ ( s ) s d s is a N-function, ΔΦ is the Φ-Laplacian operator, ϵ is a positive parameter, V : ℝN → ℝ is a continuous function, and f : ℝ → ℝ is a C1-function.
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