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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.
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참고문헌 (8)
참고문헌 신청
A.Szulkin / 1989 / Critical point theory of Ljusterni-Schnirelmann type and applications to partial di erential equations / Sem. Math. Sup. : 35 ~ 96
D.D.Hai / 2003 / On a class of semilinear elliptic systems / J. Math. Anal. Appl. 285 : 477 ~ 486
D.Lupo / 1996 / Two applications of a three critical points theorem / J. Di erential Equations 132 (2) : 222 ~ 238
Eugenio Massa / 2007 / Multiplicity results for a subperlinear elliptic system with partial interference with the spectrum / Nonlinear Anal 67 : 295 ~ 306
Jin Yinghua / 2004 / Nontrivial solutions of nonlinear elliptic equations and elliptic sys-tems / Inha U
D.D.Hai / 2003 / On a class of semilinear elliptic systems / J. Math. Anal. Appl. 285 : 477 ~ 486
D.Lupo / 1996 / Two applications of a three critical points theorem / J. Di erential Equations 132 (2) : 222 ~ 238
Eugenio Massa / 2007 / Multiplicity results for a subperlinear elliptic system with partial interference with the spectrum / Nonlinear Anal 67 : 295 ~ 306
Jin Yinghua / 2004 / Nontrivial solutions of nonlinear elliptic equations and elliptic sys-tems / Inha U
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