On a Singular Logistic Equation with the pp-Laplacian

  • Dang Dinh Hai

    Mississippi State University, USA


We prove the existence and nonexistence of positive solutions for the boundary value problems%

\left\{ \begin{alignedat}{2} -\Delta _{p}u&= g(x,u)-\frac{h(x)}{u^{\alpha }}&\quad &\text{in }\Omega \\ u&= 0&&\text{on }\partial \Omega ,% \end{alignedat}% \right.

% where Δpu=div(up2u),p>1, Ω\Delta _{p}u=\text{div}(|\nabla u|^{p-2}\nabla u),p>1,\ \Omega is a bounded domain in Rn\mathbb{R}^{n} with smooth boundary Ω\partial \Omega , % \alpha \in (0,1),g:\Omega \times (0,\infty )\rightarrow \mathbb{R} is possibly singular at u=u= 0.\ An application to a singular logistic-like equation is given.

Cite this article

Dang Dinh Hai, On a Singular Logistic Equation with the pp-Laplacian. Z. Anal. Anwend. 32 (2013), no. 3, pp. 339–348

DOI 10.4171/ZAA/1488