Existence of seven solutions for an asymptotically linear Dirichlet problem without symmetries

被引：14

作者：

Castro, Alfonso ^{[1
]}

Cossio, Jorge ^{[2
]}

Velez, Carlos ^{[2
]}

机构：

[1] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

[2] Univ Nacl Colombia Medellin, Escuela Matemat, Medellin 3840, Colombia

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2013年 / 192卷 / 04期

关键词：

Semilinear elliptic equation; Morse index; Sign-changing solutions; Bifurcation; EQUATIONS;

D O I：

10.1007/s10231-011-0239-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov-Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.

引用

页码：607 / 619

页数：13

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