Contributions to Nonlinear Elliptic Equations and Systems: A Tribute to Djairo Guedes de Figueiredo on the Occasion of his 80th Birthday PDF
Preview Contributions to Nonlinear Elliptic Equations and Systems: A Tribute to Djairo Guedes de Figueiredo on the Occasion of his 80th Birthday
Progress in Nonlinear Differential Equations and Their Applications 86 Alexandre N. Carvalho Bernhard Ruf Ederson Moreira dos Santos Jean-Pierre Gossez Sergio H.M. Soares Thierry Cazenave Editors Contributions to Nonlinear Elliptic Equations and Systems A Tribute to Djairo Guedes de Figueiredo on the Occasion of his 80th Birthday Progress in Nonlinear Differential Equations and Their Applications Volume 86 Editor HaimBrezis UniversitéPierreetMarieCurie,Paris,France Technion-IsraelInstituteofTechnology,Haifa,Israel RutgersUniversity,NewBrunswick,NJ,USA EditorialBoard AntonioAmbrosetti,ScuolaInternationaleSuperiorediStudiAvanzati, Trieste,Italy A.Bahri,RutgersUniversity,NewBrunswick,NJ,USA FelixBrowder,RutgersUniversity,NewBrunswick,NJ,USA LuisCaffarelli,TheUniversityofTexas,Austin,TX,USA Jean-MichelCoron,UniversitéPierreetMarieCurie,Paris,France LawrenceC.Evans,UniversityofCalifornia,Berkeley,CA,USA MarianoGiaquinta,UniversityofPisa,Italy DavidKinderlehrer,Carnegie-MellonUniversity,Pittsburgh,PA,USA SergiuKlainerman,PrincetonUniversity,NJ,USA RobertKohn,NewYorkUniversity,NY,USA P.L.Lions,CollégedeFrance,Paris,France JeanMawhin,UniversitéCatholiquedeLouvain,Louvain-la-Neuve, Belgium LouisNirenberg,NewYorkUniversity,NY,USA PaulRabinowitz,UniversityofWisconsin,Madison,WI,USA JohnToland,IsaacNewtonInstitute,Cambridge,UK Moreinformationaboutthisseriesathttp://www.springer.com/series/4889 Alexandre N. Carvalho (cid:129) Bernhard Ruf Ederson Moreira dos Santos (cid:129) Jean-Pierre Gossez Sergio H.M. Soares (cid:129) Thierry Cazenave Editors Contributions to Nonlinear Elliptic Equations and Systems A Tribute to Djairo Guedes de Figueiredo on the Occasion of his 80th Birthday Editors AlexandreN.Carvalho BernhardRuf InstitutodeCiênciasMatemáticasede DipartimentodiMatematica Computação UniversitádegliStudidiMilano UniversidadedeSãoPaulo Milano,Italy SãoCarlos,SP,Brazil Jean-PierreGossez EdersonMoreiradosSantos DépartementdeMathématique InstitutodeCiênciasMatemáticasede UniversitéLibredeBruxelles Computação Brussels,Belgium UniversidadedeSãoPaulo SãoCarlos,SP,Brazil ThierryCazenave SergioH.M.Soares LaboratoireJacques-LouisLions InstitutodeCiênciasMatemáticasede UniversitéPierreetMarieCurie Computação Paris,France UniversidadedeSãoPaulo SãoCarlos,SP,Brazil ISSN1421-1750 ISSN2374-0280 (electronic) ProgressinNonlinearDifferentialEquationsandTheirApplications ISBN978-3-319-19901-6 ISBN978-3-319-19902-3 (eBook) DOI10.1007/978-3-319-19902-3 LibraryofCongressControlNumber:2015946754 MathematicsSubjectClassification(2010):35A15,35J15,35J30,35J47,35J60,and35A15 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia(www. springer.com) DjairoG.deFigueiredo PhotobyChristinaFigueiredoPrudencio Preface TheICMC-SummerMeetingonDifferentialEquationsisaseriesofmeetingsthat takes place at the Instituto de Ciências Matemáticas e de Computação (ICMC) of theUniversidadedeSãoPaulo(USP)inSãoCarlos.Theyhappeneveryyear,since 1996,inthesouthernhemisphere’ssummerholidays,afewdaysbeforeCarnival. Afterthe2013Chapterofthemeeting,thelocalorganizersdecidedtodedicate thenextmeetingtothecelebrationofDjairo’s80thbirthday.WithDjairo’sblessing, the conference was arranged from the 3rd to the 7th of February, 2014, and invitations were sent out. As anyone who has ever organized a meeting knows, the hardest part is to be able to gather a large number of well-known specialists in the area, and collaborators who will help with the organization. In the case of thismeeting,wemustsaythatitwasallveryeasy.Werapidlyhadalargenumber of worldwide experts who happily agreed to participate and a large number of collaboratorswhoagreedtohelpwiththeseveraldifferentcommittees.Ofcourse, that has to do with the fact that Djairo is so well cared for in the Differential Equationscommunity. The 2014 Chapter was the largest edition ever of the meeting with over 300 participantsfrom23differentcountries,3differentcontinents,andfromallregions of Brazil. The celebration of Djairo’s 80th birthday was a very high level meeting inarelaxedandfriendlyenvironment. Just after the meeting, we decided to write this book to record this wonderful conference.WeapproachedBirkhäuseraspublishersandtheywerekeentoaccept. In compiling this volume, we have again seen the same enthusiastic behavior that weobservedduringtheorganizationofthemeeting:contributorswereeagertopay tributetoDjairo. DjairoGuedesdeFigueiredowasborninthesmalltownof“LimoeirodoNorte,” state of Ceará, Northeast Brazil, in 1934. He graduated in Civil Engineering from theUniversidadeFederaldoRiodeJaneiro,in1956.In1961,heobtainedhisPh.D. in Mathematics from the Courant Institute at NYU under the guidance of Louis Nirenberg. Hisprofessionalcareer startedin1961attheUniversidade deBrasília, in the newly built capital of Brazil. He went back to the US from 1965 to 1971, successivelyattheUniversityofWisconsininMadison,theUniversityofChicago, vii viii Preface theUniversityofMaryland,andtheUniversityofIllinoisatChicagoCircle.In1971, hecamebacktoBrazilattheUniversidadedeBrasíliaandfinallymovedin1988to UNICAMP,inCampinas,nearSãoPaulo. Djairohasaveryactivescientificlife,publishingoverahundredresearcharticles, which has made him the most cited Brazilian mathematician with almost 2500 citations in MathSciNet. His scientific contribution would be already enough to render him the dedication of a book like this one, but Djairo’s contribution to Mathematics goes far beyond that. He published 29 monographs (many of them inPortuguese)thatwereveryinfluentialtomanyyoungergenerationsofBrazilian (and many other nationalities) mathematicians. His passion for mathematics has influenced entire generations of mathematicians in Brazil, South America, and throughouttheworld.Hisdescendants,whoinclude26Ph.D.students,arealready inthefourthgeneration,andinfouryearsshouldnumber120Ph.D.s. ItissafetosaythatDjairo’sinfluenceinBrazilianmathematicsmadehimoneof thepillarsofthesubjectinthatcountry.Hehadamajorinfluenceinthedevelopment of the area of Analysis, especially in its applications to Nonlinear Elliptic Partial DifferentialEquationsandSystems,inBrazilandthroughouttheworld. Onapersonallevel,Djairoisakind,friendlypersonwithagreatsenseofhumor. His natural leadership, kindness, uprightness of character, and family values are a veryimportantpartofhislegacytotheyoungergenerations. We happily thank Djairo for the opportunity to gather together so many world- widespecialists,andforprovidingthebondswhichbroughtusthefamily-like,high levelresearchenvironmentseenthroughoutthemeeting.Weareproudtobepartof thissmalltokenofappreciationtoDjairo’sinfluenceinourlives. SãoCarlos,SP,Brazil AlexandreN.Carvalho Milano,Italy BernhardRuf SãoCarlos,SP,Brazil EdersonMoreiradosSantos Brussels,Belgium Jean-PierreGossez SãoCarlos,SP,Brazil SergioH.M.Soares Paris,France ThierryCazenave March2015 Contents Nonexistenceofpositiveclassicalsolutionsforthenonlinear Schrödingerequationwithunboundedordecayingweights................ 1 FranciscoS.B.AlbuquerqueandEveraldoS.Medeiros HylomorphicsolitonsforthegeneralizedKdVequation.................... 9 VieriBenciandDonatoFortunato AconsequenceofDjairo’sLecturesontheEkeland variationalprinciple ............................................................. 23 LucioBoccardoandLuigiOrsina WaveguidesolutionsforanonlinearSchrödingerequation withmixeddispersion ........................................................... 31 DenisBonheureandRobsonNascimento Fibersandglobalgeometryoffunctions....................................... 55 MartaCalanchi,CarlosTomei,andAndréZaccur Existence of infinitely many continua of radial singular polytropeswithgain-lossfunction.............................................. 77 AlfonsoCastroandVíctorPadrón Branchesofpositivesolutionsforsubcriticalellipticequations ............ 87 AlfonsoCastroandRosaPardo Multiplesolutionstoanisotropic criticalandsupercritical problemsinsymmetricdomains................................................ 99 MónicaClappandJorgeFaya Compactnessandnon-compactnessforYamabe-typeproblems ........... 121 FernandoCodáMarques AsymptoticsofgroundstatesforfractionalHénonsystems................. 133 David G. Costa, Olímpio H. Miyagaki, Marco Squassina, andJianfuYang ix
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