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

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 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.

Sign in / Sign up

Export Citation Format

Share Document