Geodesic
Positive solutions for some quasilinear elliptic equations with natural growths
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 1, pp. 31-39.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is $$ \begin{cases} - \text{div} ((1+ |u|^{r}) \nabla u) + |u|^{m-2} u |\nabla u|^{2} = f \quad \text{in} \, \Omega \\ u = 0 \text{su} \, \partial\Omega. \end{cases} $$
È provato un teorema di esistenza di soluzioni per una classe di equazioni ellittiche quasi-lineari, con coefficienti a crescite naturali (come suggerito dal Calcolo delle variazioni). Il problema modello è il seguente $$ \begin{cases} - \text{div} ((1+ |u|^{r}) \nabla u) + |u|^{m-2} u |\nabla u|^{2} = f \quad \text{in} \, \Omega \\ u = 0 \text{su} \, \partial\Omega. \end{cases} $$ 
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     title = {Positive solutions for some quasilinear elliptic equations with natural growths},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Boccardo, Lucio. Positive solutions for some quasilinear elliptic equations with natural growths. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 1, pp. 31-39. http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a4/

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