分数阶椭圆方程近共振问题解的多重性

Multiplicity Results for Fractional Elliptic Equations with Near Resonance

考虑当线性项的参数从右边逼近非主特征值时分数阶椭圆方程的多解性.一方面,通过对泛函在不同特征子空间上的能量水平的估计可构造出一个具有鞍点结构的解;另一方面,当参数充分接近特征值时,结合鞍点定理、Galerkin逼近方法及对近共振对应的特征子空间上能量水平的仔细估算证明第二个解的存在性.

The present paper considers the multiplicity of the solution for fractional elliptic equations when the parameter of the linear term approximates to the non-principal eigenvalue from the right.On the one hand,we establish the existence of the first solution of saddle point geometry by calculating the energy level of the functional on different eigenspaces.On the other hand,we obtain the second solution by applying the saddle theorem and the Galerkin approximation method and by evaluating the energy level on the eigenspace when the linear part is near resonance.