Handbook of differential equations. Stationary partial differential equations

625 Pages·2005·2.932 MB·English

by  Michel Chipot, Pavol Quittner

HANDBOOK
OF DIFFERENTIAL EQUATIONS
STATIONARY PARTIAL
DIFFERENTIAL EQUATIONS
VOLUME II
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H
ANDBOOK
D E
OF IFFERENTIAL QUATIONS
S P
TATIONARY ARTIAL
D E
IFFERENTIAL QUATIONS
Volume II
Editedby
M. CHIPOT
InstituteofMathematics,UniversityofZürich,Zürich,Switzerland
P. QUITTNER
DepartmentofAppliedMathematicsandStatistics,ComeniusUniversity,
Bratislava,SlovakRepublic
2005
ELSEVIER
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Preface
ThishandbookisVolumeIIinaseriesdevotedtostationarypartialdifferentialequations.
SimilarlyasVolumeI, itis acollectionof self-contained,state-of-the-artsurveyswritten
bywell-knownexpertsinthefield.
Thetopicscoveredbythishandbookincludeexistenceandmultiplicityofsolutionsof
superlinearellipticequations,bifurcationphenomena,problemswithnonlinearboundary
conditions, nonconvex problems of the calculus of variations and Schrödinger operators
withsingularpotentials.Wehopethatthesesurveyswillbeusefulforbothbeginnersand
experts and speed up the progress of corresponding (rapidly developing and fascinating)
areasofmathematics.
Wethankallthecontributorsfortheirclearlywrittenandelegantarticles.Wealsothank
ArjenSevensterandAndyDeelenatElsevierforefficientcollaboration.
M.ChipotandP.Quittner
v
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List of Contributors
Bartsch,T.,UniversitätGiessen,35392Giessen,Germany(Ch.1)
Dacorogna,B.,EPFL,1015Lausanne,Switzerland(Ch.2)
Du,Y.,UniversityofNewEngland,Armidale,NSW2351,Australia(Ch.3)
López-Gómez,J.,UniversidadComplutensedeMadrid,28040Madrid,Spain(Ch.4)
Melgaard,M.,UppsalaUniversity,S-75106Uppsala,Sweden(Ch.6)
Rossi,J.D.,UniversidaddeBuenosAires,1428BuenosAires,Argentina(Ch.5)
Rozenblum, G., Chalmers University of Technology, and University of Gothenburg,
S-41296Gothenburg,Sweden(Ch.6)
Solimini,S.,PolitecnicodiBari,70125Bari,Italy(Ch.7)
Wang,Z.-Q.,UtahStateUniversity,Logan,UT84322,USA(Ch.1)
Willem,M.,UniversitécatholiquedeLouvain,1348Louvain-la-Neuve,Belgium(Ch.1)
vii
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Contents
Preface v
ListofContributors vii
ContentsofVolumeI xi
1. TheDirichletProblemforSuperlinearEllipticEquations 1
T.Bartsch,Z.-Q.WangandM.Willem
2. NonconvexProblemsoftheCalculusofVariationsandDifferentialInclusions 57
B.Dacorogna
3. BifurcationandRelatedTopicsinEllipticProblems 127
Y.Du
4. Metasolutions:MalthusversusVerhulstinPopulationDynamics.ADream
ofVolterra 211
J.López-Gómez
5. EllipticProblemswithNonlinearBoundaryConditionsandtheSobolev
TraceTheorem 311
J.D.Rossi
6. SchrödingerOperatorswithSingularPotentials 407
G.RozenblumandM.Melgaard
7. MultiplicityTechniquesforProblemswithoutCompactness 519
S.Solimini
AuthorIndex 601
SubjectIndex 609
ix