JournalsprimsVol. 50, No. 2pp. 341–362

Positive Radial Solutions for Singular Quasilinear Elliptic Equations in a Ball

  • Dang Dinh Hai

    Mississippi State University, USA
Positive Radial Solutions for Singular Quasilinear Elliptic Equations in a Ball cover
Download PDF

Abstract

We establish the existence of positive radial solutions for the boundary value problems

{Δpu=λf(u) in B,u=0 on B,\left\{ \begin{array}{rcll} -\Delta _{p}u&=&\lambda f(u)&\text{ in }B, \\ u&=&0&\text{ on }\partial B, \end{array} \right.

where Δpu=div(up2u),p2\Delta _{p}u=\textbf{div}(|\nabla u|^{p-2}\nabla u),p\geq 2, BB is the open unit ball \mathbb{R}^{N}$$, \lambda is a positive parameter, and f:(0,)Rf:(0,\infty )\rightarrow \mathbb{R} is pp-superlinear at \infty and is allowed to be singular at 00.

Cite this article

Dang Dinh Hai, Positive Radial Solutions for Singular Quasilinear Elliptic Equations in a Ball. Publ. Res. Inst. Math. Sci. 50 (2014), no. 2, pp. 341–362

DOI 10.4171/PRIMS/136