Geodesic
Existence of positive solutions for $p(x)$-Laplacian equations with a singular nonlinear term
Electronic Journal of Differential Equations, Tome 2014 (2014).

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

Summary: 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},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     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/