Degenerate elliptic problem with a singular nonlinearity

Abstract

In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems for an elliptic equation defined by a degenerate coercive operator and a singular right hand side. \begin{equation}\label{01} \left\{ \begin{array}{lll} -\displaystyle\mbox{div}( a(x,u,\nabla u))&=\displaystyle\frac{f}{u^γ} & \mbox{ in } Ω\\ u&>0 &\mbox{ in }Ω\\ u&=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} where $\Omega$ is bounded open subset of $I{R}^N(N\ge 2),$ $\gamma >0$ and $f$ is a nonnegative function that belongs to some Lebesgue space.

References in corpus (1)

• The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity

Cited by in corpus (2)

• Nonlinear Elliptic Equations With Variable Exponents Involving Singular Nonlinearity
• Existence and regularity of positive solutions for Schrödinger-Maxwell system with singularity