Differential and Integral Equations

Singular elliptic systems with asymptotically linear nonlinearities

D.D. Hai

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We prove the existence and nonexistence of positive solutions for the system \begin{equation*} \left\{ \begin{array}{c} -\Delta u_{1}=\mu _{1}f_{1}(u_{2})\ \text{ in }\Omega , \\ -\Delta u_{2}=\mu _{2}f_{2}(u_{1}) \ \text{ in }\Omega , \\ \ \ \ \ \ \ \ u_{1}=u_{2}=0 \ \ \ \ \text{ on }\partial \Omega , \end{array} \right. \end{equation*} where $\Omega $ is a bounded domain in $\mathbb{R}^{n\text{ }}$with smooth boundary $ \partial \Omega ,$ $\mu _{i}$ are positive parameters, and $ f_{i}:(0,\infty )\rightarrow \mathbb{R}$ are asymptotically linear at $ \infty $ and allowed to be singular at $0,$ $i=1,2$.

Article information

Differential Integral Equations, Volume 26, Number 7/8 (2013), 837-844.

First available in Project Euclid: 20 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J47: Second-order elliptic systems 35J75: Singular elliptic equations


Hai, D.D. Singular elliptic systems with asymptotically linear nonlinearities. Differential Integral Equations 26 (2013), no. 7/8, 837--844. https://projecteuclid.org/euclid.die/1369057819

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