Multiplicity Results for an Anisotropic Equation with Subcritical or Critical Growth-Reference-Cited by-同舟云学术

Multiplicity Results for an Anisotropic Equation with Subcritical or Critical Growth

Published:2015-05-01 Issue:2 Volume:15 Page:377-394
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Figueiredo Giovany¹,Santos Júnior João R.¹,Suárez Antonio²

Affiliation:

1. Faculdade de Matemática Universidade Federal do Pará, CEP: 66075-110 Belém - Pa , Brazil

2. Dpto. de Ecuaciones Diferenciales y Análisis Numérico Fac. de Matemáticas, Univ. de Sevilla, C/ Tarfia s/n, 41012 - Sevilla, Spain

Abstract

Abstract In this work we show some multiplicity results for the anisotropic equation

where Ω ⊂ℝN is a bounded smooth domain, 1 < p1 ≤ p2 ≤ . . . ≤ pN and λ is a positive parameter. Using genus theory, we study the subcritical case gλ(u) = λ|u|q−2u with q ∈ (1, pN) and the critical case gλ(u) = λ|u|q−2u +|u|p*−2u with q ∈ (1, p1) and p* = N| p̅/(N−p̅), with p̅ the harmonic mean of the pi’s.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2015-0206/pdf

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