一类四阶不定微分算子的非实特征值
Non-Real Eigenvalues of a Class of Fourth Order Indefinite Differential Operators

作者: 赵馨 , 高云兰 * , 秦小娟 :内蒙古工业大学理学院,内蒙古 呼和浩特;

关键词: 不定微分算子四阶微分算子非实特征值Indefinite Differential Operator Fourth Order Differential Operator Non-Real Eigenvalue

摘要: 本文讨论了一类四阶正则不定微分算子的非实特征值,在系数可积的条件下分别给出了权函数仅变号一次和权函数可变号任意次时非实特征值的界。

Abstract: The present paper deals with non-real eigenvalues of regular fourth order indefinite differential operators. Bounds of non-real eigenvalues are obtained under mild integrable conditions of coefficients when weighted function’s sign changes one or any time.

文章引用: 赵馨 , 高云兰 , 秦小娟 (2017) 一类四阶不定微分算子的非实特征值。 应用数学进展, 6, 664-669. doi: 10.12677/AAM.2017.65078

参考文献

[1] Richardson, R.G.D. (1918) Contributions to the Study of Oscillatory Properties of the Solutions of Linear Differential Equations of the Second Order. American Journal of Mathematics, 40, 283-316.
https://doi.org/10.2307/2370485

[2] Turyn, L. (1980) Sturm-Liouville Problems with Several Parameters. Journal of Differential Equations, 38, 239-259.
https://doi.org/10.1016/0022-0396(80)90007-8

[3] Binding, P. and Volkmer, H. (1996) Eigencurves for Two-Parameter Sturm-Liouville Equations. SIAM Review, 38, 27-48.
https://doi.org/10.1137/1038002

[4] Binding, P. and Browne, P.J. (1988) Applications of Two Parameter Spectral Theory to Symmetric Generalised Eigenvalue Problem. Applicable Analysis, 29, 107-142.
https://doi.org/10.1080/00036818808839776

[5] Xie, B. and Qi, J. (2013) Non-Real Eigenvalues of Indefinite Sturm-Liouville Problems. Journal of Differential Equations, 255, 2291-2301.
https://doi.org/10.1016/j.jde.2013.06.013

[6] Behrndt, J., Chen, S., Philipp, F. and Qi, J. (2014) Estimates on the Non-Real Eigenvalues of Regular Indefinite Sturm-Liouville Problems. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, A144, 1113-1126.
https://doi.org/10.1017/S0308210513001212

[7] Han, X. and Gao, T. (2016) A Priori Bounds and Existence of Non-Real Eigenvalues of Fourth-Order Boundary Value Problem with Indefinite Weight Function. Journal of Differential Equations, 82, 1-9.

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