Differential and Integral Equations

On a class of nonvariational elliptic systems with nonhomogenous boundary conditions

Sebastián Lorca, Pedro Pedro, and João Marcos do Ó

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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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35J55 53C35: Symmetric spaces [See also 32M15, 57T15]


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

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