scholarly journals Uniform Sobolev inequalities for second order non-elliptic differential operators

2016 ◽  
Vol 302 ◽  
pp. 323-350 ◽  
Author(s):  
Eunhee Jeong ◽  
Yehyun Kwon ◽  
Sanghyuk Lee
Keyword(s):  
Differential Operators ◽  
Second Order ◽  
Sobolev Inequalities ◽  
Elliptic Differential Operators

Oscillation criteria of Nehari-type for Sturm–Liouville operators and elliptic differential operators of second order and the lower spectrum

1988 ◽  
Vol 109 (1-2) ◽  
pp. 127-144 ◽  
Author(s):  
F. Fiedler
Keyword(s):  
Differential Equation ◽  
Differential Operators ◽  
Second Order ◽  
Oscillation Criteria ◽  
Elliptic Differential Equations ◽  
Ordinary Differential Operators ◽  
Elliptic Differential Operators ◽  
Sturm Liouville ◽  
Lower Spectrum ◽  
Liouville Operators

SynopsisSufficient oscillation criteria of Nehari-type are established for the differential equation −uʺ(t) + q(t)u(t) = 0, 0<t<∞, with and without sign restrictions on q(t), respectively. These results are extended to Sturm-Liouville equations and elliptic differential equations of second order.In Section 7 we present conclusions for the lower spectrum of elliptic differential operators and also for the discreteness of the spectrum of certain ordinary differential operators of second order.

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