Year: 2000
Type: book-chapter
Abstract: We discuss a broad class of second order quasilinear elliptic operators on $$ {\mathbb{R}^N} $$ acting from the Sobolev space $$ {W^{2,p}}({\mathbb{R}^N}) $$ into $$ {L^p}({\mathbb{R}^N}) $$ for p ∈ (N∞). Conditions are given which ensure that such operators are C1—Fredholm maps of index zero. Then we give additional assumptions which imply that they are proper on the closed bounded subsets of $$ {W^{2,p}}({\mathbb{R}^N}) $$ . For operators with these properties the topological degrees developed by Fitzpatrick, Pejsachowicz and Rabier are available. We illustrate their use by deriving results about the bifurcation of connected components of solutions of quasilinear elliptic equations on $$ {\mathbb{R}^N} $$ .
Source: Birkhäuser Basel eBooks
Authors: Patrick J. Rabier, Charles A. Stuart
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2024785484