LEADER 04235nam 22006735 450 001 9910484551003321 005 20250610110056.0 010 $a3-030-45603-X 024 7 $a10.1007/978-3-030-45603-0 035 $a(CKB)4100000011273849 035 $a(MiAaPQ)EBC6213735 035 $a(DE-He213)978-3-030-45603-0 035 $a(PPN)248397958 035 $a(MiAaPQ)EBC6213680 035 $a(MiAaPQ)EBC29091090 035 $a(EXLCZ)994100000011273849 100 $a20200529d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCritical Point Theory $eSandwich and Linking Systems /$fby Martin Schechter 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (347 pages) 311 08$a3-030-45602-1 320 $aIncludes bibliographical references and index. 327 $aPreface -- Linking Systems -- Sandwich Systems -- Linking Sandwich Sets -- The Monotonicity Trick -- Infinite Dimensional Linking -- Differential Equations -- Schrödinger Equations -- Zero in the Spectrum -- Global Solutions -- Second Order Hamiltonian Systems -- Core Functions -- Custom Monotonicity Methods -- Elliptic Systems -- Flows and Critical Points -- The Semilinear Wave Equation -- Nonlinear Optics -- Radially Symmetric Wave Equations -- Multiple Solutions. 330 $aThis monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author?s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book?s main subject: applications to problems in mathematics and physics. These include topics such as Schrödinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used. 606 $aMathematical optimization 606 $aOperator theory 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aOptimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26008 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical optimization. 615 0$aOperator theory. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aOptimization. 615 24$aOperator Theory. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aAnalysis. 676 $a514.74 700 $aSchechter$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$013643 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484551003321 996 $aCritical Point Theory$92070426 997 $aUNINA