04235nam 22006735 450 991048455100332120250610110056.03-030-45603-X10.1007/978-3-030-45603-0(CKB)4100000011273849(MiAaPQ)EBC6213735(DE-He213)978-3-030-45603-0(PPN)248397958(MiAaPQ)EBC6213680(MiAaPQ)EBC29091090(EXLCZ)99410000001127384920200529d2020 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCritical Point Theory Sandwich and Linking Systems /by Martin Schechter1st ed. 2020.Cham :Springer International Publishing :Imprint: Birkhäuser,2020.1 online resource (347 pages)3-030-45602-1 Includes bibliographical references and index.Preface -- 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.This 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.Mathematical optimizationOperator theoryGlobal analysis (Mathematics)Manifolds (Mathematics)Mathematical analysisAnalysis (Mathematics)Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26008Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Mathematical optimization.Operator theory.Global analysis (Mathematics)Manifolds (Mathematics)Mathematical analysis.Analysis (Mathematics).Optimization.Operator Theory.Global Analysis and Analysis on Manifolds.Analysis.514.74Schechter Martinauthttp://id.loc.gov/vocabulary/relators/aut13643MiAaPQMiAaPQMiAaPQBOOK9910484551003321Critical Point Theory2070426UNINA