更高分数阶p-Laplacian方程的特征值问题
Eigenvalue Problems of Higher Fractional Order p-Laplacian Equation
摘要: 特征值、特征向量一直都是谱理论的重要组成部分。为了得到更高分数阶p-Laplacian算子相关的结果，我们将通过变分法、约束变分法证明方程对应的泛函满足Palais-Smale条件，并借助相关定理将求解特征值转化为求解泛函的临界值，最终得到了在所定义空间中算子的特征值、特征向量。
Abstract: Eigenvalues and eigenvectors are always important components of spectral theory. In order to obtain the results related to higher fractional order p-Laplacian operators, we will prove that the functional corresponding to the equation satisfies the Palais-Salale condition by using the varia-tional method and constrained variational method, and transform the solution of eigenvalue into the critical value of the solution of functional by using the relevant theorem, and finally obtain the eigenvalue and eigenvector of the operator in the defined space.
文章引用：杨飒, 魏公明. 更高分数阶p-Laplacian方程的特征值问题[J]. 理论数学, 2023, 13(3): 526-532. https://doi.org/10.12677/PM.2023.133056

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