## Differential and Integral Equations

- Differential Integral Equations
- Volume 8, Number 2 (1995), 393-403.

### A priori estimates and uniqueness of inflection points for positive solutions of semipositone problems

#### Abstract

We prove that positive solutions of $-\Delta u = \lambda f(u)$ in $\Omega$ and $u = 0$ on $\partial \Omega$ where $f$ is increasing, concave, and $f(0) < 0$ satisfy $c_{1} \leq {\lambda f(d) \over d} \leq c_{2}$ where $d = \sup u.$ Also, we show that solutions of the above have exactly one inflection point.

#### Article information

**Source**

Differential Integral Equations, Volume 8, Number 2 (1995), 393-403.

**Dates**

First available in Project Euclid: 20 May 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1369083476

**Mathematical Reviews number (MathSciNet)**

MR1296131

**Zentralblatt MATH identifier**

0816.34028

**Subjects**

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations

Secondary: 34B15: Nonlinear boundary value problems 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

#### Citation

Iaia, Joseph A. A priori estimates and uniqueness of inflection points for positive solutions of semipositone problems. Differential Integral Equations 8 (1995), no. 2, 393--403. https://projecteuclid.org/euclid.die/1369083476