On the existence results for a class of singular elliptic system involving indefinite weight functions and asymptotically linear growth forcing term
Resumen
In this work, we study the existence of positive solutions to the singular system$$
\left\{\begin{array}{ll}
-\Delta_{p}u = \lambda a(x)f(v)-u^{-\alpha} & \textrm{ in }\Omega,\\
-\Delta_{p}v = \lambda b(x)g(u)-v^{-\alpha} & \textrm{ in }\Omega,\\
u = v= 0 & \textrm{ on }\partial \Omega,
\end{array}\right.
$$
where $\lambda $ is positive parameter, $\Delta_{p}u=\textrm{div}(|\nabla u|^{p-2} \nabla u)$, $p>1$, $ \Omega \subset R^{n} $ some for $ n >1 $, is a bounded domain with smooth boundary $\partial \Omega $ , $ 0<\alpha< 1 $, and $f,g: [0,\infty] \to\R$ are continuous, nondecreasing functions which are asymptotically $ p $-linear at $\infty$. We prove the existence of a positive solution for a certain range of $\lambda$ using the method of sub-supersolutions.
Descargas
La descarga de datos todavía no está disponible.
Publicado
2017-09-23
Número
Sección
Research Articles
Derechos de autor 2017 Boletim da Sociedade Paranaense de Matemática

Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).