Geodesic
Existence of solutions to $p$-Laplace equations with logarithmic nonlinearity
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This article concerns the the nonlinear elliptic equation $$ -\hbox{div}(|\nabla u|^{p-2}\nabla u) =\log u^{p-1}+\lambda f(x,u) $$ in a bounded domain $\Omega \subset \mathbb{R}^{N}$ with $N\geq 1$ and $u=0$ on $\partial\Omega$. By means of a double perturbation argument, we obtain a nonnegative solution.
Classification : 35B20, 35B65, 35J65
Keywords: existence, logarithmic nonlinearity, supersolution, subsolution 
@article{EJDE_2009__2009__a33,
     author = {Mo, Jing and Yang, Zuodong},
     title = {Existence of solutions to $p${-Laplace} equations with logarithmic nonlinearity},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a33/}
}
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Mo, Jing; Yang, Zuodong. Existence of solutions to $p$-Laplace equations with logarithmic nonlinearity. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a33/