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Kahler einstein metrics and integral invariants - (lecture notes in math volume 1314) - paper, 1988 Lecture Notes in Mathematics Series, Vol. 1314

Langue : Anglais

Auteur :

Couverture de l’ouvrage Kahler einstein metrics and integral invariants - (lecture notes in math volume 1314) - paper
The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.
Introduction Notation Chapter 1. Evolutionary equations. Results on existance 1.1 The (generalized Korteweg-de Vries equation (KdVE) 1.2 The nonlinear Schrödinger equation (NLSE) 1.3 On the blowing up of solutions 1.4 Additional remarks Chapter 2. Stationary problems 2.1 Existence of solutions. An ODE approach 2.2 Existence of solutions. A variational method 2.3 The concentration-compactness method of P.L. Lions 2.4 On basis properties of systems of solutions 2.5 Additional remarks Chapter 3. Stability of solutions 3.1 Stability of soliton-like solutions 3.2 Stability of kinks for the KdVE 3.3 Stability of solutions of the NLSE non-vanishing as (x) to infinity 3.4 Additional remarks Chapter 4. Invariant measures 4.1 On Gaussian measures in Hilbert spaces 4.2 An invariant measure for the NLSE 4.3 An infinite series of invariant measures for the KdVE 4.4 Additional remarks Bibliography Index

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