Table Of ContentLecture Notes ni
Mathematics
Edited yb .A Dold dna .B Eckmann
964
Ordinary and Partial
Differential Equations
Proceedings of the Seventh Conference
Held at Dundee, Scotland, March 29-April ,2 1982
Edited by .W .N Everitt dna B.D. Sleeman
galreV-regnirpS
nilreB Heidelberg New kroY 1982
Editors
W.N. Everitt
Department of Mathematics, University of Birmingham
RO. Box 363. Birmingham B15 2TT, England
B. D. Sleeman
Department of Mathematics, University of Dundee
Dundee 1DD 4HN, Scotland
AMS Subject Classifications (1980): 34-06, 35-06
ISBN 3-54041968-X Springer-Verlag Berlin Heidelberg NewYork
ISBN 0-38741968-X Springer-Verlag NewYork Heidelberg Berlin
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© yb Springer-Verlag Berlin Heidelberg 1982
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D E D I C A T I O N
These Proceedings are dedicated to
The University of Dundee
on the occasion of the centenary celebrations
1882 - 1982
PREFACE
These Proceedings form a record of the lectures delivered at the seventh
Conference on Ordinary and Partial Differential Equations which was held at the
University of Dundee, Scotland during the week Monday 29 March to Friday 2 April
1982.
The Conference formed part of the centenary celebrations for the University of
Dundee 1882-1982. The University of W~rzburg was officially represented at the
Conference, for this purpose, by Professor Dr H W Knobloch.
The Conference was attended by 120 mathematicians from more than 25 countries.
The Conference was organised by a Committee with membership: E R Dawson,
W N Everitt, B D Sleeman.
Following again the tradition set by the earlier Dundee Conferences the
Organising Committee named as Honorary Presidents of the 1982 Conference
Professor Jean Mawhin (Belgium)
Professor Tung Chin-Chu (P R China).
The Committee expresses its gratitude to all mathematicians who took part in
the work of the Conference.
The Committee thanks : the University of Dundee for generously supporting the
Conference; the Warden, Domestic Bursar and Staff of West Park Hall for all their
help in providing accommodation for the participants; the Department of Mathematical
Sciences for continuing support for the Conference; the Bursar of Residences, the
Accommodation Officer, the Information Officer and the Finance Officer of the
University.
The Committee offers special thanks to the Vice-Principal of the University,
Professor P D Griffiths, for representing the University at the opening ceremony,
and at the University reception held for all participants.
The Committee records with gratitude financial support, in the form of travel
and subsistence funds, from
The Royal Society of London
and
The European Research Office of the United States Army.
Vl
The Professors Everitt and Sleeman record special thanks to their colleague
Commander E R Dawson R N whose services, from retirement, were generously offered in
helping to organise the Conference, and who carried the main responsibility for the
accommodation of all participants in West Park Hall. Commander ~awson also edited a
number of the manuscripts submitted for publication in these Proceedings.
Likewise special thanks are due to all the Secretaries in the Department of
Mathematical Sciences of the University; in particular to Mrs Caroline Peters for
her invaluable contribution.
W N Everitt B D Sleeman
C O N T E N T S
' V Atkinson:
n) the asymptotic behaviour of the Titchmarsh-Weyl m-coefficient and the
~pectral function for scalar second-order differential expressions ........ 1
V Atkinson and C T Fulton:
;ome limit circle eigenvalue problems and asymptotic formulae for
~igenvalues ............................................................... 28
V Atkinson, J R Haddock and 0 J Staffans:
integral inequalities and exponential convergence of solutions of
lifferential equations with bounded delay ................................. 56
) L Barrow and P W Bates:
~ifurcation of periodic travelling waves for a reaction-diffusion system .. 69
I Behncke:
Nle Dirac equation with an anomalous magnetic moment II ................... 77
I Benci, A Capozzi and D Fortunato:
)eriodic solutions of a class of Hamiltonian systems ...................... 86
J Browne:
4ultiparameter problems : the last decade ................................. 95
C Brown:
~n approach to the Dirichlet index for operators satisfying minimal
:onditions ................................................................ Ii0
I A Burns and E M Cliff and J M Amillo Gil
qonlinear neutral functional differential equations in product spaces ..... 118
• A Clarkson and J B McLeod:
k connection formula for the second Painlev~ transcendent ................. 135
) Colton:
Fhe inverse scattering problem for acoustic waves ......................... 143
7 Dubois and P Morales:
?n the Hukuhara-Kneser property for some Cauchy problems in locally convex
topological vector spaces ................................................. 162
X D~ng:
Essential self-adjointness and self-adjointness for generalized
Bchr~dinger operators ..................................................... 171
lllV
M S P Eastham:
Asymptotic theory for a critical class of fourth-order differential
equations ................................................................. 179
Elbert:
Oscillation and nonoscillation theorems for some nonlinear ordinary
differential equations .................................................... 187
D E Edmunds:
Entropy numbers, s-numbers and eigenvalues ................................ 213
P C Fife and B Nicolaenko:
The singular perturbation approach to flame theory with chain and
competing reactions ....................................................... 232
J Fleckinger:
On the singular values of non-self-adjoint operators of SchrZdinger type .. 251
I M Gali:
Optimal control of systems governed by elliptic operator of infinite order 263
V B Goyal and P W Schaefer:
Comparison principles for some fourth order elliptic problems ............. 272
R C Grimmer and W Schappacher:
Weak solutions of integrodifferential equations and applications .......... 280
D B Hinton and J K Shaw:
Titchmarsh's l-dependent boundary conditions for Hamiltonian systems ...... 298
F A Howes:
318
Exterior boundary value problems for perturbed equations of elliptic type .
H G Kaper, C Gerrit Lekkerkerker and A Zettl:
Linear transport theory and an indefinite Sturm-Liouville problem ......... 326
R M Kauffman:
Non-normalizable eigenfunction expansions for ordinary differential
operators ................................................................. 362
H W Knobloch:
Some aspects and recent developments in linear control theory ............. 368
I W Knowles:
Eigenvalue problems and the Riemann zeta-function ......................... 388
XI
M A Kon and L A Raphael:
Superposition principles and pointwise evaluation of Sturm-Liouville
eigenfunction expansions .................................................. 406
K Kreith:
Qualitative theory of hyperbolic characteristic initial value problems I ... 416
R T Lewis:
Applications of a comparison theorem for quasi-accretive operators in a
Hilbert space ............................................................. 422
L L Littlejohn and A M Krall:
A singular sixth order differential equation with orthogonal polynomial
eigenfunctions ............................................................ 435
S-O LondOn:
On the asymptotics of some Volterra equations with locally finite
measures and large perturbations .......................................... 445
J Mawhin:
Periodic oscillations of forced pendulum-like equations ................... 458
R C MacCamy and E Stephan:
A simple layer potential method for three-dimensional eddy current problems 477
A C McBride:
Index laws for some ordinary differential operators .......................
485
P A McCoy:
Converse initial value problems for a class of heat equations .............
494
J R McLaughlin:
Higher order inverse eigenvalue problems .................................. 503
A B Mingarelli:
Indefinite Sturm-Liouville problems ....................................... 519
S E A Mohammed:
The infinitesimal generator of a stochastic functional differential
equation ..................................................................
529
M Nakao:
On solutions to the initial-boundary problem for perturbed porous medium
equation ..................................................................
539
X
F Neuman:
A survey of global properties of linear differential equations of the
n-th order ................................................................ 548
D Pascali:
Strongly nonlinear evolution variational inequalities ..................... 564
D Race:
A further result on the essential spectrum of linear 2nth order
differential expressions with complex coefficients ........................ 569
R Rautmann:
On error bounds for nonstationary spectral Navier-Stokes approximations ... 576
T T Read:
Sectorial second order differential operators ............................. 584
H R~h:
Spectral mapping theorems for dissipative Co-semigroup generators ......... 591
D A S~nchez:
Some preliminary results on periodic solutions of matrix Riccati equations 598
R Saxton:
Solitary and travelling waves in a rod .................................... 603
K Seitz:
Investigations in the theory of partial differential equations of infinite
order ..................................................................... 609
J K Shaw and D B Hinton:
Well-posed boundary problems for Hamiltonian systems of limit point or
limit circle type ......................................................... 614
K Soni:
On uniform asymptotic expansion of a class of integral transforms ......... 632
R L Sternberg~ M J Goldstein and D Drinkard:
On a new numerical method for a new class of nonlinear partial
differential equations arising in nonspherical geometrical optics ......... 642
A Z-A M Tazali:
Local existence theorems for ordinary differential equations of
fractional order .......................................................... 652
Tung Chin-Chu:
Application of the theorem of connectivity of M 7 in astronomy ............. 666
Xl
L Turyn:
Perturbations of periodic boundary conditions ............................. 675
A Vanderbauwhede:
Bifurcation problems with triangular symmetry ............. . ............... 686
J Walter:
On the foundations of thermodynamics ...................................... 695
A D Wood and R B Paris:
On some conjectures on the deficiency index for symmetric differential
operators ................................................................. 703
S D Wray:
On a second-order differential expression and its Dirichlet integral ...... 710
E M E Zayed:
An inverse eigenvalue problem for the Laplace operator .................... 718
