Geodesic
Existence of positive solutions for \(p(x)\)-Laplacian equations with a singular nonlinear term
Electronic journal of differential equations, Tome 2014 (2014)
In this article, we study the existence of positive solutions for the $p(x)$-Laplacian Dirichlet problem

$ -\Delta _{p(x)}u=\lambda f(x,u) $

in a bounded domain $\Omega \subset \mathbb{R}^{N}$. The singular nonlinearity term f is allowed to be either $f(x,s)\to +\infty $, or $f(x,s)\to +\infty $ as $s\to 0^{+}$ for each $x\in \Omega $. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent interest.
Classification : 35J25, 35J65, 35J70
Keywords: $p(x)$-Laplacian, singular nonlinear term, sub-supersolution method 
@article{EJDE_2014__2014__a99,
     author = {Liu,  Jingjing and Zhang,  Qihu and Zhao,  Chunshan},
     title = {Existence of positive solutions for {\(p(x)\)-Laplacian} equations with a singular nonlinear term},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1298.35086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a99/}
}
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Liu,  Jingjing; Zhang,  Qihu; Zhao,  Chunshan. Existence of positive solutions for \(p(x)\)-Laplacian equations with a singular nonlinear term. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a99/