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Minimax Systems and Critical Point Theory

:	Martin Schechter
:	Minimax Systems and Critical Point Theory
:	Birkhäuser Basel
:	9780817649029
:	1
:	CHF 47.80
:

:	Analysis
:	English

:	242
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.

	Contents	6
	Preface	10
	Critical Points of Functionals	14
	1.1 Introduction	14
	1.2 Extrema	15
	1.3 PalaisÒSmale sequences	15
	1.4 Cerami sequences	16
	1.5 Linking sets	16
	1.6 Previous definitions of linking	17
	1.7 Notes and remarks	18
	Minimax Systems	19
	2.1 Introduction	19
	2.2 Definitions and theorems	20
	2.3 Linking subsets	21
	2.4 A variation	23
	2.5 Weaker conditions	24
	2.6 Some consequences	25
	2.7 Notes and remarks	27
	Examples of Minimax Systems	28
	3.1 Introduction	28
	3.2 A method using homeomorphisms	28
	3.3 A method using metric spaces	30
	3.4 A method using homotopy-stable families	30
	3.5 Examples of linking sets	32
	3.6 Various geometries	35
	3.7 A sandwich theorem	37
	3.8 Notes and remarks	40
	Ordinary Differential Equations	41
	4.1 Extensions of PicardÌs theorem	41
	4.2 Estimating solutions	43
	4.3 Extending solutions	44
	4.4 The proofs	45
	4.5 An important estimate	46
	The Method Using Flows	48
	5.1 Introduction	48
	5.2 Theorem 2.4	48
	5.3 Theorem 2.12	50
	5.4 Theorem 2.14	53
	5.5 Theorem 2.21	54
	Finding Linking Sets	60
	6.1 Introduction	60
	6.2 The strong case	61
	6.3 The remaining proofs	63
	6.4 Notes and remarks	65
	Sandwich Pairs	66
	7.1 Introduction	66
	7.2 Criteria	67
	7.3 Notes and remarks	70
	Semilinear Problems	71
	8.1 Introduction	71
	8.2 Bounded domains	71
	8.3 Some useful quantities	77
	8.4 Unbounded domains	79
	8.5 Further applications	83
	8.6 Special cases	88
	8.7 The proofs	89
	8.8 Notes and remarks	91
	Superlinear Problems	92
	9.1 Introduction	92
	9.2 The main theorems	93
	9.3 Preliminaries	95
	9.4 Proofs	96
	9.5 The parameter problem	99
	9.6 The monotonicity trick	104
	9.7 Notes and remarks	111
	Weak Linking	113
	10.1 Introduction	113
	10.2 Another norm	114
	10.3 Some examples	118
	10.4 Some applications	120
	10.5 Notes and remarks	132
	Fucik Spectrum: Resonance	134
	11.1 Introduction	134
	11.2 The curves	136
	11.3 Existence	140
	11.4 Notes and remarks	144
	Rotationally Invariant Solutions	145
	12.1 Introduction	145
	12.2 The spectrum of the linear operator	146
	12.3 The nonlinear case	148
	12.4 Notes and remarks	151
	Semilinear Wave Equations	152
	13.1 Introduction	152
	13.2 Convexity and lower semi-continuity	152
	13.3 Existence of saddle points	155
	13.4 Criteria for convexity	158
	13.5 Partial derivatives	159
	13.6 The theorems	161
	13.7 The proofs	161
	13.8 Notes and remarks	164
	Type (II) Regions	165
	14.1 Introduction	165
	14.2 The asymptotic equation	168
	14.3 Local estimates	170
	14.4 The solutions	174
	14.5 Notes and remarks	177
	Weak Sandwich Pairs	178
	15.1 Introduction	178
	15.2 Weak sandwich pairs	179
	15.3 Applications	185
	15.4 Notes and remarks	191
	Multiple Solutions	192
	16.1 Introduction	192
	16.2 Two examples	192
	16.3 Statement of the theorems	193
	16.4 Some lemmas	195
	16.5 Local linking	207
	16.6 The proofs	209
	16.7 Notes and remarks	210
	Second-Order Periodic Systems	213
	17.1 Introduction	213
	17.2 Proofs of the theorems	215
	17.3 Nonconstant solutions	221
	17.4 Notes and remarks	226
	Bibliography	228
	Index	239