Measures of Noncompactness and Condensing Operators - ISBN:3764327162

Measures of Noncompactness and Condensing Operators

Date: 21 April 2011, 14:23

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TABLE OF CONTENTS
Introduction VB
Chapter 1. MEASURES OF NONCOMPACTNESS 1
1.1. The Kuratowski and Hausdorff measures of noncompactness 1
1.2. The general notion of measure of noncompactness 9
1.3. The measure of noncompactness (3 13
1.4. Sequential measures of noncompactness 17
1.5. Condensing operators 21
1.6. Ultimately compact operators 27
1.7. K-operators 35
1.8. Survey of the literature 44
Chapter 2. THE LINEAR THEORY 53
2.1. Fredholm operators 53
2.2. The "+" -operation and normal measures of noncompactncss 55
2.3. Fredholmness criteria for operators 57
2.4. The (psi1,psi2)-norms of an operator 61
2.5. The measure of noncompactness of the conjugate operator 67
2.6. The Fredholm spectrum of a bounded linear operator 73
2.7. Normal measures of noncompactness and perturbation theory
for linear operators 81
2.8. Survey of the literature 04
Chapter 3. THE FIXED-POINT INDEX OF CONDENSING OPERATORS 09
3.1. Definitions and properties of the index 99
3.2. Examples of computation of the index of a condensing operator 105
3.3. Linear and differentiable condensing operators 107
3.4. Further properties of the index
3.5. Generalization of the notion of index to various classes of maps
3.6. The index of operators in locally convex spaces
3.7. The relative index
3.8. The index of positive operators
3.9. Survey of the literature
Chapter 4. APPLICATIONS
4.1. Differential equations in Banach space
4.2. Ito stochastic equations with deviating argument
4.3. The Cauchy problem for equations of neutral type
4.4. Periodic solutions of an equation of neutral point with small delay
4.5. The averaging principle for equations of neutral type
4.6. On the stability of solutions of equations of neutral type
4.7. Floquet theory for equations of neutral type
4.8. Continuous dependence of the Floquet exponents on the delay
4.9. Measures of noncompactness and condensing operators in spaces of
integrable functions
References
Subject index

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