Asymptotic theory and deficiency indices for fourth and higher order self-adjoint equations: A simplified approach

1981 ◽  
pp. 88-99 ◽  
Author(s):  
M. S. P. Eastham ◽  
C. G. M. Grudniewicz
Keyword(s):  
Asymptotic Theory ◽  
Higher Order ◽  
Adjoint Equations ◽  
Simplified Approach ◽  
Deficiency Indices

On the number of solutions of right-definite problems with a convergent Dirichlet integral

1982 ◽  
Vol 91 (3-4) ◽  
pp. 347-360 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
The Other ◽  
Dirichlet Integral ◽  
Number Of Solutions ◽  
Linearly Independent ◽  
Higher Order Differential Equations

SynopsisA recently developed asymptotic theory of higher-order differential equations is applied to problems of right-definite type to determine the numbers M+, M− of linearly independent solutions with a convergent Dirichlet integral, M+ and M− referring to the usual upper and lower λ.-half-planes. Particular attention is given to the phenomenon noted by Karlsson in which one of M+ and M− is maximal but not the other. Conditions are given under which M+ (say) is maximal and M− is the same, one less, and two less.

Higher‐order special self‐adjoint equations and particle dynamics

1983 ◽  
Vol 24 (10) ◽  
pp. 2433-2437 ◽  
Author(s):  
James L. Reid ◽  
John R. Ray
Keyword(s):  
Particle Dynamics ◽  
Higher Order ◽  
Adjoint Equations
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