Nonlinear Analysis and Semilinear Elliptic ProblemsCambridge University Press, 4 janv. 2007 Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises. |
Table des matières
| 241 | |
Section 2 | 252 |
Section 3 | 259 |
Section 4 | 262 |
Section 5 | 263 |
Section 6 | 272 |
Section 7 | 274 |
Section 8 | 275 |
Section 9 | 282 |
Section 10 | 286 |
Section 11 | 302 |
Section 12 | 306 |
Expressions et termes fréquents
Appendix arguments assume assumption bifurcation boundary bounded function c₁ class C¹ compact concentrate consider constant contradiction converges critical levels critical points defined denote dimensional eigenvalue elliptic equations essential spectrum example exists Furthermore Heaviside function hence holds implicit function theorem implies infimum J(un JR(u Lagrange's theorem Lemma lim inf maximum principle Moreover non-negative nonlinear notation p+1 JRn perturbation positive solutions problem proof of Theorem Proposition A5.3 prove Rn Rn satisfies scalar curvature Section sequence smooth Sobolev inequality solution of A4.1 sufficiently large sufficiently small Suppose symmetric tends to zero Theorem A2.1 u(xx un)n uniformly vortex core wɛ(z Wr² Yamabe problem zero at infinity Ζε μα Σλ Σμ Σο Φε ди