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Type: | Artigo |
Title: | An elliptic system and the critical hyperbola |
Author: | Ferreira, Lucas C. F. Medeiros, Everaldo Montenegro, Marcelo |
Abstract: | We consider a nonlinear elliptic system of Lane-Emden type in the whole space ℝn , namely (Formula presented). Our region for (p,q ) covers in particular the critical and supercritical cases with respect to the critical hyperbola (Formula presented) + (Formula presented) + (Formula presented)= (Formula presented). We prove existence of solutions for f ∈ Ld (ℝn), by means of a fixed point technique in the Lebesgue space Lr1 × Lr2. Our results allow unbounded solutions without Hs -regularity. The solutions are shown to be classical and positive when f is smooth enough and positive. Moreover, if f is radial or odd (or even), we prove that the solutions preserve these properties. Also, it is shown that the solutions (u,v ) are nonradial when f is nonradial. We consider a nonlinear elliptic system of Lane-Emden type in the whole space Rn, namely ( ∆u + v|v|p−1 = 0, x ∈Rn, ∆v + u|u|q−1 + f = 0, x ∈Rn. Our region for (p,q) covers in particular the critical and supercritical cases with respect to the critical hy |
Subject: | Equações diferenciais elipticas Existência de solução (Equações diferenciais) Lp-espaços |
Country: | Estados Unidos |
Editor: | American Institute of Mathematical Sciences |
Citation: | Communications On Pure And Applied Analysis. American Institute Of Mathematical Sciences, v. 14, n. 3, p. 1169 - 1182, 2015. |
Rights: | fechado fechado |
Identifier DOI: | 10.3934/cpaa.2015.14.1169 |
Address: | http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10900 |
Date Issue: | 2015 |
Appears in Collections: | IMECC - Artigos e Outros Documentos |
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