四阶不定微分算子非实特征值的估计
Estimates on the Non-Real Eigenvalues of Fourth Order Indefinite Differential Operators
DOI: 10.12677/PM.2017.73017, PDF,    国家自然科学基金支持
作者: 胡帆*, 孙炯, 李昆, 郝晓玲：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 四阶微分算子；非实特征值；不定权函数；Fourth Order Differential Operators； Non-Real Eigenvalue； Indefinite Weight Function
摘要: 本文研究了一类关于四阶微分算子非实特征值的估计。利用算子理论和经典分析，研究了由权函数变号产生的不定微分算子的特征值问题，对权函数具有多个拐点时和只有一个拐点的情况分别进行了讨论,得到非实特征值实部和虚部的估计。
Abstract: The present paper gives an estimate on the non-real eigenvalues for a class of fourth order differential operators. Using operator theory and classical analysis, we study the eigenvalue problem for indefinite differential operators produced by the signs of weight function, and discuss the cases of many turning points and a turning point for the weight function respectively, then we get the estimate on the real and imaginary parts of the non-real eigenvalues.
文章引用：胡帆, 孙炯, 李昆, 郝晓玲. 四阶不定微分算子非实特征值的估计[J]. 理论数学, 2017, 7(3): 141-148. https://doi.org/10.12677/PM.2017.73017

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