Nontrivial solutions for an elliptic system
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In this work, we consider an elliptic system\begin{eqnarray}\left\{ \begin{array}{cc}-\triangle u = au + bv + \delta_1 u^+ -\delta_2 u^- +f_1 (x,u,v) \qquad \text{ in } \Omega, \\-\triangle v = bu + cv + \eta_1 v^+ -\eta_2 v^- +f_2 (x,u,v) \qquad \text{ in } \Omega, \\u=v=0 \qquad \qquad \qquad \text{ on } \partial \Omega,\end{array}\right. \nonumber\end{eqnarray}where $\Omega \subset R^{N}$ be a bounded domain with smoothboundary. We prove that the system has at leasttwo nontrivial solutions by applying linking theorem.
Abstract
In this work, we consider an elliptic system\begin{eqnarray}\left\{ \begin{array}{cc}-\triangle u = au + bv + \delta_1 u^+ -\delta_2 u^- +f_1 (x,u,v) \qquad \text{ in } \Omega, \\-\triangle v = bu + cv + \eta_1 v^+ -\eta_2 v^- +f_2 (x,u,v) \qquad \text{ in } \Omega, \\u=v=0 \qquad \qquad \qquad \text{ on } \partial \Omega,\end{array}\right. \nonumber\end{eqnarray}where $\Omega \subset R^{N}$ be a bounded domain with smoothboundary. We prove that the system has at leasttwo nontrivial solutions by applying linking theorem.
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