LEADER 05197nam 22009135 450 001 9910983385903321 005 20251031124241.0 010 $a9789819795390 010 $a9819795397 024 7 $a10.1007/978-981-97-9539-0 035 $a(MiAaPQ)EBC31897888 035 $a(Au-PeEL)EBL31897888 035 $a(CKB)37465303000041 035 $a(DE-He213)978-981-97-9539-0 035 $a(OCoLC)1500771322 035 $a(EXLCZ)9937465303000041 100 $a20250206d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLocalization Approaches in Strongly Indefinite Problems /$fby Yanheng Ding, Tian Xu 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (598 pages) 225 1 $aSeries in Contemporary Mathematics,$x2364-0103 ;$v6 311 08$a9789819795383 311 08$a9819795389 327 $aChapter 1. Variational Problems ?? A Brief Retrospective -- Chapter 2. Strongly Indefinite Problems ?? Examples and Motivations -- Chapter 3. Localized Energy Estimates for Strongly Indefinite Functionals -- Chapter 4. Semiclassical Standing Waves of Nonlinear Dirac Equations -- Chapter 5. Effect of External Potentials in a Coupled System Reaction-Diffusion -- Chapter 6. The Spinorial Brezis-Nirenberg Problem -- Chapter 7. Isometrically Embedded Sphere with Prescribed Mean Curvature -- Chapter 8. Further Problems with Strongly Indefinite Structures. 330 $aSeveral important problems arising in Physics, Differential Geometry and other topics lead to consider semilinear variational equations of strongly indefinite type and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments and non-degenerate structure, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. This book discusses some new abstract methods together with their applications to several localization problems, whose common feature is to involve semilinear partial differential equations with a strongly indefinite structure. This book deals with a variety of partial differential equations, including nonlinear Dirac equation from quantum physics (which is of first order), coupled system of multi-component incongruent diffusion and spinorial Yamabe type equations on spin manifolds. The unified framework in this book covers not only the existence of solutions to these PDEs problems, but also asymptotic behaviors of these solutions. In particular, the results for the nonlinear Dirac equations show several concentration behaviors of semiclassical standing waves under the effect of external potentials and the results for the spinorial Yamabe type equations show the existence of conformal embeddings of the 2-sphere into Euclidean 3-space with prescribed mean curvature. This book will be appealing to a variety of audiences including researchers, postdocs, and advanced graduate students who are interested in strongly indefinite problems. 410 0$aSeries in Contemporary Mathematics,$x2364-0103 ;$v6 606 $aDifferential equations 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aMathematical optimization 606 $aCalculus of variations 606 $aGeometry, Differential 606 $aQuantum theory 606 $aDifferential Equations 606 $aGlobal Analysis and Analysis on Manifolds 606 $aCalculus of Variations and Optimization 606 $aDifferential Geometry 606 $aQuantum Physics 606 $aEquacions diferencials$2thub 606 $aAnālisi global (Matemātica)$2thub 606 $aOptimitzaciķ matemātica$2thub 606 $aCālcul de variacions$2thub 606 $aGeometria diferencial$2thub 606 $aTeoria quāntica$2thub 608 $aLlibres electrōnics$2thub 615 0$aDifferential equations. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aGeometry, Differential. 615 0$aQuantum theory. 615 14$aDifferential Equations. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aCalculus of Variations and Optimization. 615 24$aDifferential Geometry. 615 24$aQuantum Physics. 615 7$aEquacions diferencials 615 7$aAnālisi global (Matemātica) 615 7$aOptimitzaciķ matemātica 615 7$aCālcul de variacions 615 7$aGeometria diferencial 615 7$aTeoria quāntica 676 $a515.35 700 $aDing$b Yanheng$01784409 701 $aXu$b Tian$01784410 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983385903321 996 $aLocalization Approaches in Strongly Indefinite Problems$94316032 997 $aUNINA