Positive solutions for some quasilinear elliptic equations with natural growths

Lucio Boccardo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: 1, page 31-39
  • ISSN: 1120-6330

Abstract

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We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is - div ⁢ 1 + u r ⁢ ∇ ⁡ u + u m - 2 ⁢ u ⁢ ∇ ⁡ u 2 = f in ⁢ Ω u = 0 su ⁢ ∂ ⁡ Ω .

How to cite

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Boccardo, Lucio. "Positive solutions for some quasilinear elliptic equations with natural growths." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.1 (2000): 31-39. <http://eudml.org/doc/252345>.

@article{Boccardo2000,
abstract = {We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is $$ \begin\{cases\} - \text\{div\} ((1+ |u|^\{r\}) \nabla u) + |u|^\{m-2\} u |\nabla u|^\{2\} = f \quad &\text\{in\} \, \Omega \\ u = 0 &\text\{su\} \, \partial\Omega. \end\{cases\} $$},
author = {Boccardo, Lucio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Quasilinear elliptic equations; Natural growth coefficients; Euler-Lagrange equations; natural growth coefficients},
language = {eng},
month = {3},
number = {1},
pages = {31-39},
publisher = {Accademia Nazionale dei Lincei},
title = {Positive solutions for some quasilinear elliptic equations with natural growths},
url = {http://eudml.org/doc/252345},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Boccardo, Lucio
TI - Positive solutions for some quasilinear elliptic equations with natural growths
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/3//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 1
SP - 31
EP - 39
AB - We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is $$ \begin{cases} - \text{div} ((1+ |u|^{r}) \nabla u) + |u|^{m-2} u |\nabla u|^{2} = f \quad &\text{in} \, \Omega \\ u = 0 &\text{su} \, \partial\Omega. \end{cases} $$
LA - eng
KW - Quasilinear elliptic equations; Natural growth coefficients; Euler-Lagrange equations; natural growth coefficients
UR - http://eudml.org/doc/252345
ER -

References

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