Handbook of differential equations. Stationary PDEs

617 Pages·2008·2.41 MB·English

by  Michel Chipot

HANDBOOK
OF DIFFERENTIAL EQUATIONS
STATIONARY PARTIAL
DIFFERENTIAL EQUATIONS
VOLUME V
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H
ANDBOOK
D E
OF IFFERENTIAL QUATIONS
S P
TATIONARY ARTIAL
D E
IFFERENTIAL QUATIONS
Volume V
Editedby
M. CHIPOT
InstituteofMathematics,UniversityofZürich,Zürich,Switzerland
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Preface
This handbook is the fifth volume in the series devoted to stationary partial differential
equations. As the preceding volumes, it is a collection of self-contained, state-of-the-art
surveyswrittenbywell-knownexpertsinthefield.
Thetopicscoveredbythisvolumeincludeinparticularsemilinearandsuperlinearellip-
ticsystems,thefiberingmethodfornonlinearvariationalproblems,somenonlineareigen-
valueproblems,thestudiesofthestationaryBoltzmannequationandtheGierer–Meinhardt
system.Ihopethatthesesurveyswillbeusefulforbothbeginnersandexpertsandhelpto
thediffusionoftheserecentdeepresultsinmathematicalscience.
I would like to thank all the contributors for their elegant articles. I also thank Lauren
SchultzYuhaszandMaraVos-SarmientoatElsevierfortheexcellenteditingworkofthis
volume.
M.Chipot
v
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List of Contributors
deFigueiredo,D.G.,IMECC-Unicamp,C.P.6065Campinas,S.Paulo13081-970,Brazil
[email protected](Ch.1)
Pohozaev,S.I.,SteklovMathematicalInstitute,RussianAcademyofSciences,Gubkinastr.
8,119991Moscow,Russia(Ch.2)
Ruf, B., Dipartimento de Matematica, Università degli Studi di Milano, Via Saldini 50,
I-20133Milano,Italy(Ch.3)
Suzuki,T.,DivisionofMathematicalScience,DepartmentofSystemsInnovation,Gradu-
ateSchoolofScience,OsakaUniversity,Japan(Ch.4)
Takahashi, F., Department of Mathematics, Faculty of Science, Osaka City University,
Japan(Ch.4)
Ukai, S., Department of Mathematics and Liu Bie Ju Centre for Mathematical Sciences,
CityUniversityofHongKong,83TatCheeAvenue,Kowloon,HongKong(Ch.5)
Wei,J.,DepartmentofMathematics,TheChineseUniversityofHongKong,Shatin,Hong
Kong(Ch.6)
Yang, T., Department of Mathematics and Liu Bie Ju Centre for Mathematical Sciences,
CityUniversityofHongKong,83TatCheeAvenue,Kowloon,HongKong(Ch.5)
vii
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Contents
Preface v
ListofContributors vii
ContentsofVolumeI xi
ContentsofVolumeII xiii
ContentsofVolumeIII xv
ContentsofVolumeIV xvii
1. SemilinearEllipticSystems:Existence,Multiplicity,SymmetryofSolutions 1
D.G.deFigueiredo
2. NonlinearVariationalProblemsviatheFiberingMethod 49
S.I.Pohozaev
3. SuperlinearEllipticEquationsandSystems 211
B.Ruf
4. NonlinearEigenvalueProblemwithQuantization 277
T.SuzukiandF.Takahashi
5. StationaryProblemofBoltzmannEquation 371
S.UkaiandT.Yang
6. ExistenceandStabilityofSpikesfortheGierer–MeinhardtSystem 487
J.Wei
AuthorIndex 587
SubjectIndex 593
ix