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Critical point theorysandwich and li...

Schechter, Martin.

Critical point theorysandwich and linking systems /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Critical point theoryby Martin Schechter.
其他題名:	sandwich and linking systems /
作者:	Schechter, Martin.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xxxvi, 320 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Critical point theory (Mathematical analysis)
電子資源:	https://doi.org/10.1007/978-3-030-45603-0
ISBN:	9783030456030$q(electronic bk.)

Critical point theorysandwich and linking systems /
Schechter, Martin.

Critical point theorysandwich and linking systems /[electronic resource] :by Martin Schechter. - Cham :Springer International Publishing :2020. - xxxvi, 320 p. :ill., digital ;24 cm.

Preface -- Linking Systems -- Sandwich Systems -- Linking Sandwich Sets -- The Monotonicity Trick -- Infinite Dimensional Linking -- Differential Equations -- Schrodinger 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 Schrodinger 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.

ISBN: 9783030456030$q(electronic bk.)

Standard No.: 10.1007/978-3-030-45603-0doiSubjects--Topical Terms:

189986
Critical point theory (Mathematical analysis)

LC Class. No.: QA614.7 / .S343 2020

Dewey Class. No.: 515.64

Critical point theorysandwich and linking systems /
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505 0 $a Preface -- Linking Systems -- Sandwich Systems -- Linking Sandwich Sets -- The Monotonicity Trick -- Infinite Dimensional Linking -- Differential Equations -- Schrodinger 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.
520 $a 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 Schrodinger 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.
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