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September/October 2011 On a class of nonvariational elliptic systems with nonhomogenous boundary conditions
Sebastián Lorca, Pedro Pedro, João Marcos do Ó
Differential Integral Equations 24(9/10): 845-860 (September/October 2011).

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)).$

Citation

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Sebastián Lorca. Pedro Pedro. João Marcos do Ó. "On a class of nonvariational elliptic systems with nonhomogenous boundary conditions." Differential Integral Equations 24 (9/10) 845 - 860, September/October 2011.

Information

Published: September/October 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35127
MathSciNet: MR2850368

Subjects:
Primary: 35J55, 35J65, 53C35

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.24 • No. 9/10 • September/October 2011
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