scholarly journals An asymptotic theory of higher-order operator differential equations with nonsmooth nonlinearities

2004 ◽  
Vol 217 (2) ◽  
pp. 448-488 ◽  
Author(s):  
Vladimir Kozlov (Linköping) ◽  
Vladimir Maz'ya (Linköping)
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
Order Operator

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.

On the eigenvectors for a class of matrices arising from quasi-derivatives

1984 ◽  
Vol 97 ◽  
pp. 73-78 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
Symmetric Matrices ◽  
Convenient Formula ◽  
Class Of Matrices ◽  
Higher Order Differential Equations

SynopsisLet A be a product of symmetric matrices, A = RQ, with R non-singular, and let v be an eigenvector of A. For certain R and Q, a convenient formula for the expression (R−1v)tv is obtained. This expression occurs in the diagonalization of A and, in the particular case where A is associated with the quasi-derivative formulation of higher-order differential equations, the expression occurs in the asymptotic theory of solutions of the differential equation.

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