Fourth order elliptic system with dirichlet boundary condition
نویسنده
چکیده
* Correspondence: tsjung@kunsan. ac.kr Department of Mathematics, Kunsan National University, Kunsan 573-701, Korea Full list of author information is available at the end of the article Abstract We investigate the multiplicity of the solutions of the fourth order elliptic system with Dirichlet boundary condition. We get two theorems. One theorem is that the fourth order elliptic system has at least two nontrivial solutions when lk <c < lk+1 and lk+n(lk+n c) < a + b < lk+n+1(lk+n+1 c). We prove this result by the critical point theory and the variation of linking method. The other theorem is that the system has a unique nontrivial solution when lk <c <lk+1 and lk(lk c) < 0, a+b < lk+1(lk+1 c). We prove this result by the contraction mapping principle on the Banach space. AMS Mathematics Subject Classification: 35J30, 35J48, 35J50
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