数学
有界函数
特征向量
多重性(数学)
山口定理
索波列夫空间
变分原理
领域(数学分析)
纯数学
数学分析
数学物理
物理
量子力学
非线性系统
标识
DOI:10.1016/j.cnsns.2023.107174
摘要
We consider the following class of non-local superlinear parametric problem (−Δ)su=λu+u+2s∗−1+f(x),inΩ,u=0,inRN∖Ω,where 02s and 2s∗=2N/(N−2s) is the fractional critical Sobolev exponent, u+(x)≔max{u(x),0} and λ>0 is a parameter. When λ is not an eigenvalue of (−Δ)s and N>6s, we apply variational methods (especially Linking Theorem) to show that the above problem has at least two non-trivial solutions. We also discuss the existence results of resonant problem (that is, λ=λ1,s with λ1,s is the principal eigenvalue of (−Δ)s) via Ekeland variational principle.
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