Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs

Cover......Page 1
Half Title......Page 2
Series Page......Page 3
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 8
 1.1 Measures of Noncompactness......Page 10
 1.2 The Brouwer Fixed-Point Theorem. The Schauder Fixed-Point Theorem......Page 20
 1.3 Fixed Points of Strict Set Contractions......Page 29
 1.4 The Kronecker Index......Page 34
  1.5.1 Smooth Mappings......Page 43
  1.5.2 Homotopy Invariance......Page 48
  1.5.3 Continuous Mappings. Basic Properties......Page 51
  1.5.4 The Case f:∂D⊂nℝ →Sn − 1.......Page 58
 1.6 The Leray-Schauder Degree......Page 61
 1.7 The Fixed-Point Index for Completely Continuous Mappings......Page 65
 1.8 The Fixed-Point Index for Strict Set Contractions......Page 66
 1.9 Multiple Fixed-Point Theorems......Page 73
 2.1 Periodic Solutions for First Order ODEs......Page 92
 2.2 BVPs for First Order ODEs......Page 111
 2.3 BVPs for Second Order ODEs......Page 128
 2.4 BVPs with Impulses......Page 132
 3.1 Global Existence for a Class of Fractional-Differential Equations......Page 146
 3.2 Multiple Solutions for a BVP of Nonlinear Riemann-Liouville Fractional Differential Equations......Page 162
 3.3 Multiple Solutions for a BVP of Nonlinear Caputo Fractional Differential Equations......Page 175
 4.1 Differentiability of Classical Solutions with Respect to the Initial Conditions of an IVP......Page 178
 4.2 Local Existence of Classical Solutions for an IBVP......Page 191
 4.3 Periodic Solutions......Page 209
 4.4 Multiple Solutions for an IBVP with Robin Boundary Conditions......Page 222
 5.1 Differentiability of Classical Solutions with Respect to the Initial Conditions for an IVP for a Class of Hyperbolic Equations......Page 230
 5.2 Multiple Solutions for an IBVP with Robin Boundary Conditions......Page 247
 5.3 Periodic Solutions......Page 254
 6.1 Multiple Solutions for a BVP with Robin Boundary Conditions......Page 266
 6.2 Existence and Smoothness of Navier-Stokes Equations......Page 273
Bibliography......Page 302
Index......Page 304