### Boundary blow up for semilinear elliptic equations with nonlinear gradient terms

#### Abstract

The paper deals with the equation $\Delta u \pm |\nabla u|^q = f (u)$ in $\Omega \subset \mathbf{R}^n$, where $u$ blows up at the boundary $\partial \Omega$ and $\Omega$ is a bounded domain, which satisfies an interior and an exterior sphere condition. The existence and the asymptotic behaviour of $u$ near the boundary are investigated, showing how the nonlinear gradient term affects the results.

#### Article information

Source
Adv. Differential Equations Volume 1, Number 1 (1996), 133-150.

Dates
First available in Project Euclid: 25 April 2013

Mathematical Reviews number (MathSciNet)
MR1357958

Zentralblatt MATH identifier
0840.35034

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B40: Asymptotic behavior of solutions

#### Citation

Bandle, Catherine; Giarrusso, Ester. Boundary blow up for semilinear elliptic equations with nonlinear gradient terms. Adv. Differential Equations 1 (1996), no. 1, 133--150.https://projecteuclid.org/euclid.ade/1366896318