scholarly journals Non-real eigenvalues of symmetric Sturm–Liouville problems with indefinite weight functions

2017 ◽  
pp. 1-14
Author(s):  
Bing Xie ◽  
Huaqing Sun ◽  
Xinwei Guo
Keyword(s):  
Weight Functions ◽  
Indefinite Weight ◽  
Indefinite Weight Functions ◽  
Sturm Liouville

scholarly journals Estimates on the non-real eigenvalues of regular indefinite Sturm–Liouville problems

2014 ◽  
Vol 144 (6) ◽  
pp. 1113-1126 ◽  
Author(s):  
Jussi Behrndt ◽  
Shaozhu Chen ◽  
Friedrich Philipp ◽  
Jiangang Qi
Keyword(s):  
Differential Expression ◽  
Weight Functions ◽  
Indefinite Weight ◽  
The Real ◽  
Indefinite Weight Functions ◽  
Sturm Liouville ◽  
Explicit Bounds

Regular Sturm–Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this paper we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the differential expression.

scholarly journals On the existence results for a class of singular elliptic system involving indefinite weight functions and asymptotically linear growth forcing term

2017 ◽  
Vol 37 (3) ◽  
pp. 67-74
Author(s):  
Ghasem A. Afrouzi ◽  
S. Shakeri ◽  
N. T. Chung
Keyword(s):  
Linear Growth ◽  
Smooth Boundary ◽  
Singular System ◽  
Existence Results ◽  
Weight Functions ◽  
Indefinite Weight ◽  
Asymptotically Linear ◽  
Existence Of Positive Solutions ◽  
Indefinite Weight Functions ◽  
Nondecreasing Functions

In this work, we study the existence of positive solutions to the singular system$$\left\{\begin{array}{ll}-\Delta_{p}u = \lambda a(x)f(v)-u^{-\alpha} & \textrm{ in }\Omega,\\-\Delta_{p}v = \lambda b(x)g(u)-v^{-\alpha} & \textrm{ in }\Omega,\\u = v= 0 & \textrm{ on }\partial \Omega,\end{array}\right.$$where $\lambda $ is positive parameter, $\Delta_{p}u=\textrm{div}(|\nabla u|^{p-2} \nabla u)$, $p>1$, $ \Omega \subset R^{n} $ some for $ n >1 $, is a bounded domain with smooth boundary $\partial \Omega $ , $ 0<\alpha< 1 $, and $f,g: [0,\infty] \to\R$ are continuous, nondecreasing functions which are asymptotically $ p $-linear at $\infty$. We prove the existence of a positive solution for a certain range of $\lambda$ using the method of sub-supersolutions.

scholarly journals Modified moments for indefinite weight functions

1990 ◽  
Vol 57 (1) ◽  
pp. 607-624 ◽  
Author(s):  
Gene H. Golub ◽  
Martin H. Gutknecht
Keyword(s):  
Weight Functions ◽  
Indefinite Weight ◽  
Indefinite Weight Functions ◽  
Modified Moments
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