
Perturbation Methods and Semilinear Elliptic Problems on R^n
Birkhäuser (Publisher)
Published on 18. November 2005
Book
Hardback
XII, 184 pages
978-3-7643-7321-4 (ISBN)
Description
Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R 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, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a natural perturbation parameter, like inthe bifurcationfromthe essentialspectrum orinsingularlyperturbed equations or in the study of semiclassical standing waves for NLS. In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies. For these perturbation problems a speci?c approach,that takes advantage of such a perturbative setting, seems the most appropriate. These abstract tools are provided by perturbation methods in critical point theory. Actually, it turns out that such a framework can be used to handle a large variety of equations, usually considered di?erent in nature. Theaimofthismonographistodiscusstheseabstractmethodstogetherwith their applications to several perturbation problems, whose common feature is to n involve semilinear Elliptic Partial Di?erential Equations on R with a variational structure.
More details
Series
Edition
2006 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XII, 184 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 17 mm
Weight
465 gr
ISBN-13
978-3-7643-7321-4 (9783764373214)
DOI
10.1007/3-7643-7396-2
Schweitzer Classification
Other editions
Additional editions

Antonio Ambrosetti | Andrea Malchiodi
Perturbation Methods and Semilinear Elliptic Problems on R^n
E-Book
03/2006
1st Edition
Birkhäuser
€53.49
Available for download
Persons
Prof. Shair Ahmad is a professor of Mathematics at the University of Texas, San Antonio.
Prof. Antonio Ambrosetti is full professor of Mathematical Analysis at SISSA, Trieste, Italy.
Content
Examples and Motivations.- Pertubation in Critical Point Theory.- Bifurcation from the Essential Spectrum.- Elliptic Problems on ?n with Subcritical Growth.- Elliptic Problems with Critical Exponent.- The Yamabe Problem.- Other Problems in Conformal Geometry.- Nonlinear Schrödinger Equations.- Singularly Perturbed Neumann Problems.- Concentration at Spheres for Radial Problems.