Geodesic
Existence of solutions to \(p\)-Laplace equations with logarithmic nonlinearity
Electronic journal of differential equations, Tome 2009 (2009)
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__a133,
     author = {Mo,  Jing and Yang,  Zuodong},
     title = {Existence of solutions to {\(p\)-Laplace} equations with logarithmic nonlinearity},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1175.35067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a133/}
}
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JO  - Electronic journal of differential equations
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VL  - 2009
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%A Yang,  Zuodong
%T Existence of solutions to \(p\)-Laplace equations with logarithmic nonlinearity
%J Electronic journal of differential equations
%D 2009
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%G en
%F EJDE_2009__2009__a133
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__a133/