On a class of nonlinear elliptic equations. (English) Zbl 0819.35051

Chipot, M.

Bojarski, Bogdan (ed.) et al., Partial differential equations. Part 1. The 36th semester held at the Stefan Banach International Mathematical Center in Warsaw, Poland, from September 17 to December 17, 1990. Warsaw: Polish Academy of Sciences, Inst. of Mathematics. Banach Cent. Publ. 27, Part 1, 75-80 (1992).

Let \(\Omega\) be a bounded domain of \(\mathbb{R}^ n\) with boundary \(\Gamma\), \(n\geq 1\). The goal of this note is to summarize results regarding existence and number of solutions of the equation \[ \Delta\varphi- |\nabla \varphi|^ q+ \lambda \varphi^ p=0 \quad \text{in }\Omega, \qquad \varphi>0 \quad \text{in }\Omega, \qquad \varphi=0 \quad \text{on }\Gamma, \tag{1} \] \(\lambda>0\), \(p,q>1\).
For the entire collection see [Zbl 0771.00021].

MSC:

35J65

Nonlinear boundary value problems for linear elliptic equations

Keywords:

multiplicity of solutions