### Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations

#### Abstract

We establish two general nonlinear Liouville theorems for equations of the type $$-\Delta u=h(x_1)f(u),\; u\geq 0 \; \mbox{ in } R^N,\; \sup_{R^N}u < +\infty.$$ We then show how these Liouville theorems can be used to obtain a priori estimates for positive solutions of indefinite superlinear elliptic equations for several new cases left open in previous research.

#### Article information

Source
Adv. Differential Equations Volume 10, Number 8 (2005), 841-860.

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2150868

Zentralblatt MATH identifier
1161.35388

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B45: A priori estimates

#### Citation

Du, Yihong; Li, Shujie. Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations. Adv. Differential Equations 10 (2005), no. 8, 841--860.https://projecteuclid.org/euclid.ade/1355867821