## Advances in Differential Equations

- Adv. Differential Equations
- Volume 14, Number 5/6 (2009), 401-432.

### Positive solutions for equations and systems with $p$-Laplace like operators

M. García-Huidobro, J. R. J. R. Ward, and R. Manásevich

#### Abstract

We prove the existence of positive solutions to boundary-value problems of the form \begin{align*} \begin{gathered} (\phi(u'))'+f(t,u)=0,\quad t\in(0,1)\\ \theta(u(0))=\beta \theta(u'(0)), \quad \theta(u(1))=-\delta \theta(u'(1)), \quad \beta,\delta\ge 0, \end{gathered} \end{align*} where $\phi$ and $\theta$ are odd increasing homeomorphisms of the real line. We also prove the existence of positive solutions to related systems. Our approach is via a priori estimates and Leray-Schauder degree.

#### Article information

**Source**

Adv. Differential Equations, Volume 14, Number 5/6 (2009), 401-432.

**Dates**

First available in Project Euclid: 18 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355867255

**Mathematical Reviews number (MathSciNet)**

MR2502700

**Zentralblatt MATH identifier**

1185.34028

**Subjects**

Primary: 34B15: Nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems

#### Citation

García-Huidobro, M.; Manásevich, R.; J. R. Ward, J. R. Positive solutions for equations and systems with $p$-Laplace like operators. Adv. Differential Equations 14 (2009), no. 5/6, 401--432. https://projecteuclid.org/euclid.ade/1355867255