Weak convergence methods for semilinear elliptic equations:
This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonl...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific Pub. Co.
c1999
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| Subjects: | |
| Online Access: | FHN01 Volltext |
| Summary: | This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrödinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais–Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration–compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik–Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions |
| Physical Description: | xi, 234 p. ill |
| ISBN: | 9789812815064 |
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| 520 | |a This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrödinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais–Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration–compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik–Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions | ||
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| id | DE-604.BV044636449 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:49Z |
| institution | BVB |
| isbn | 9789812815064 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030034421 |
| oclc_num | 1012650764 |
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| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xi, 234 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Chabrowski, Jan 1941- Verfasser aut Weak convergence methods for semilinear elliptic equations Jan Chabrowski Singapore World Scientific Pub. Co. c1999 xi, 234 p. ill txt rdacontent c rdamedia cr rdacarrier This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrödinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais–Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration–compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik–Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions Nonlinear boundary value problems / Numerical solutions Convergence Differential equations, Elliptic Erscheint auch als Druck-Ausgabe 9789810240769 Erscheint auch als Druck-Ausgabe 9810240767 http://www.worldscientific.com/worldscibooks/10.1142/4225#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Chabrowski, Jan 1941- Weak convergence methods for semilinear elliptic equations Nonlinear boundary value problems / Numerical solutions Convergence Differential equations, Elliptic |
| title | Weak convergence methods for semilinear elliptic equations |
| title_auth | Weak convergence methods for semilinear elliptic equations |
| title_exact_search | Weak convergence methods for semilinear elliptic equations |
| title_full | Weak convergence methods for semilinear elliptic equations Jan Chabrowski |
| title_fullStr | Weak convergence methods for semilinear elliptic equations Jan Chabrowski |
| title_full_unstemmed | Weak convergence methods for semilinear elliptic equations Jan Chabrowski |
| title_short | Weak convergence methods for semilinear elliptic equations |
| title_sort | weak convergence methods for semilinear elliptic equations |
| topic | Nonlinear boundary value problems / Numerical solutions Convergence Differential equations, Elliptic |
| topic_facet | Nonlinear boundary value problems / Numerical solutions Convergence Differential equations, Elliptic |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4225#t=toc |
| work_keys_str_mv | AT chabrowskijan weakconvergencemethodsforsemilinearellipticequations |