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

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。 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.