## Differential and Integral Equations

### On a class of nonvariational elliptic systems with nonhomogenous boundary conditions

#### Abstract

Using a fixed--point theorem of cone expansion/compression type, we show the existence of at least three positive radial solutions for the class of quasi-- linear elliptic systems \begin{equation*} \left\{ \begin{array}{rclcl} -\Delta_p u & = & \lambda k_1(|x|) f(u,v) & \mbox{ in } & \Omega, \\ -\Delta_q v & = & \lambda k_2(|x|) g(u,v) & \mbox{ in } & \Omega, \\ ( u,v) & = & (a,b) & \mbox{ on } & \partial \Omega \end{array} \right. \end{equation*} where the nonlinearities $f, g \in C([0, +\infty)^2; [0,+\infty))$ are superlinear at zero and sublinear at $+ \infty.$ The parameters $\lambda, a$ and $b$ are positive, $\Omega$ is the ball in $\mathbb{R}^N$, with $N \ge 3,$ of radius $R_0$ which is centered at the origin, $1< p, \; q\le 2$, and $k_1, k_2 \in C ([0, R_0]; [0, +\infty)).$

#### Article information

Source
Differential Integral Equations, Volume 24, Number 9/10 (2011), 845-860.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356012888

Mathematical Reviews number (MathSciNet)
MR2850368

Zentralblatt MATH identifier
1249.35127

#### Citation

do Ó, João Marcos; Lorca, Sebastián; Pedro, Pedro. On a class of nonvariational elliptic systems with nonhomogenous boundary conditions. Differential Integral Equations 24 (2011), no. 9/10, 845--860. https://projecteuclid.org/euclid.die/1356012888