Nontrivial solutions for an elliptic system
Main Article Content
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 smooth
boundary. We prove that the system has at least
two nontrivial solutions by applying linking theorem.
Article Details
Supporting Agencies
References
[1] A.Szulkin, Critical point theory of Ljusterni-Schnirelmann type and applications to partial differential equations. Sem. Math. Sup., Vol. 107, pp. 35–96, Presses Univ. Montreal, Montreal, QC, 1989. Google Scholar
[2] D.D.Hai, On a class of semilinear elliptic systems, J. Math. Anal. Appl., 285 (2003), 477–486. Google Scholar
[3] D.Lupo and A.M.Micheletti, Two applications of a three critical points theorem, J. Differential Equations 132 (2) (1996), 222–238. Google Scholar
[4] Eugenio Massa, Multiplicity results for a subperlinear elliptic system with partial interference with the spectrum, Nonlinear Anal. 67(2007), 295–306. Google Scholar
[5] Hyewon Nam, Multiplicity results for the elliptic system using the minimax the- orem, Korean J. Math. 16 (2008) (4), 511–526. Google Scholar
[6] Jin Yinghua, Nontrivial solutions of nonlinear elliptic equations and elliptic sys- tems, Inha U. 2004. Google Scholar
[7] Yukun An, Mountain pass solutions for the coupled systems of second and fourth order elliptic equations, Nonlinear Anal. 63 (2005), 1034–1041. Google Scholar
[8] Zou, Wenming, Multiple solutions for asymptotically linear elliptic systems. J. Math. Anal. Appl. 255 (2001) (1), 213–229. Google Scholar