Generalized solutions for nonlinear elliptic equations.

El Hachimi, Abderrahmane; Igbida, Jaouad; Jamea, Ahmed

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Nonlinear parabolic problems with Neumann-type boundary conditions and $L^{1}$ -data.

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Positive solutions for some quasilinear elliptic equations with natural growths

Lucio Boccardo (2000)

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

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We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is $\{\begin{matrix} - div ((1 + {|u|}^{r}) \nabla u) + {|u|}^{m - 2} u {|\nabla u|}^{2} = f & in Ω \\ u = 0 & su \partial Ω . \end{matrix}$