Spectral Analysis of Higher-Order Differential Operators II: Fourth-Order Equations

1999 ◽  
Vol 59 (1) ◽  
pp. 188-206 ◽  
Author(s):  
Christian Remling
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Differential Operators ◽  
Higher Order ◽  
Fourth Order Equations

scholarly journals A Kneser Theorem for Higher order Elliptic Equations

1977 ◽  
Vol 20 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. Allegretto
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Higher Order ◽  
Second Order ◽  
Oscillation Criteria ◽  
Fourth Order Equations ◽  
Oscillation Theorems

The problem of establishing oscillation and non-oscillation criteria for elliptic equations has recently been considered by several authors. Extensive bibliographies may be found in the books by C. A. Swanson, [7], and by K. Kreith, [3].Most of the interest has so far centered on equations of second order with some results also established for fourth order equations. Non-oscillation theorems for higher order equations have recently been established by the author, [1], and by Noussair and Yoshida, [5]. In particular, both in [1] and [5], Kneser-type theorems were established for classes of higher order elliptic equations.

A Note on the Numerical Solution of Fourth Order Differential Equations

1954 ◽  
Vol 5 (4) ◽  
pp. 176-184 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Numerical Method ◽  
Fourth Order ◽  
Flow Equation ◽  
Higher Order ◽  
Relaxation Procedure ◽  
Fourth Order Equations ◽  
Correction Terms

SummaryAn old numerical method of solving fourth order differential equations is put in relaxation form. The higher order correction terms are included and the technique is illustrated by an example. The method has the advantage of being more rapidly convergent than the usual relaxation procedure for fourth order equations. Some comments are made on the numerical solution of the viscous flow equation.

scholarly journals Spectral Analysis of Higher-Order Differential Operators with Discontinuity Conditions at an Interior Point

2017 ◽  
Vol 63 (2) ◽  
pp. 362-372
Author(s):  
V A Yurko
Keyword(s):  
Spectral Analysis ◽  
Interior Point ◽  
Differential Operators ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Higher Order ◽  
Jump Conditions ◽  
Discontinuity Conditions

Higher-order differential operators on a finite interval with jump conditions inside the interval are studied. Properties of spectral characteristics are obtained, and completeness and expansion theorems are proved for this class of operators.

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