分数阶椭圆型算子系统在非主特征值处近共振的多重解

Multiplicity results for some fractional elliptic type systems near resonance with a nonprincipal eigenvalue

研究分数阶椭圆型系统特征值的性质,对Sobolev空间进行直和分解,并利用临界点理论中的环绕定理和局部鞍点定理,得到了分数阶椭圆型算子系统在非主特征值处近共振的多重解存在性的结论。

The fractional elliptic type systems are studied. According to the chareteristics of the eigenvalues for a class of fractional elliptic type systems, the Sobolev space is resolved;Some multiplicity results of solutions are obtained for a class of fractional elliptic type systems near resonance with a nonprincipal eigenvalues by classical link theorem and a local saddle point theorem in critical theory.