| Preface |
| Introduction |
| Equations of Barbashin Type / Chapter I.： |
| Differential equations in Banach spaces / 1.： |
| Integro-differential equations of Barbashin type / 1.1.： |
| The evolution operator / 1.2.： |
| Special cases and examples / 1.3.： |
| Some auxiliary results / 1.4.： |
| Degenerate kernels / 1.5.： |
| Symmetric kernels / 1.6.： |
| Barbashin equations in the space C / 2.： |
| Linear operators in the space C / 2.1.： |
| The spaces [characters not reproducible] / 2.2.： |
| Compact and weakly compact operators / 2.3.： |
| Strongly continuous operator functions / 2.4.： |
| Norm-continuous operator functions / 2.5.： |
| Representation of the evolution operator / 2.6.： |
| Stamping and infra-stamping operators / 2.7.： |
| Barbashin equations in Lebesgue spaces / 3.： |
| Linear operators in the space L[subscript p] / 3.1.： |
| The space [characters not reproducible characters not reproducible](L[subscript p]) / 3.2.： |
| Sufficient conditions for regularity / 3.3.： |
| Barbashin equations in ideal spaces / 3.4.： |
| Ideal spaces / 4.1.： |
| Functions of two variables and vector functions / 4.2.： |
| Barbashin operators in ideal spaces / 4.3.： |
| The space [characters not reproducible characters not reproducible](X) / 4.4.： |
| Some spectral theory for Barbashin operators / 4.5.： |
| Theory of Linear Barbashin Equations / Chapter II.： |
| Stability of solutions / 5.： |
| Ljapunov and Ljapunov-Bohl exponents / 5.1.： |
| Perturbation of the Ljapunov-Bohl exponent / 5.2.： |
| Application to Barbashin operators / 5.3.： |
| Ljapunov functions / 5.4.： |
| Continuous dependence on parameters / 6.： |
| Continuous dependence of the evolution operator / 6.1.： |
| The first Bogoljubov theorem / 6.2.： |
| Smooth dependence / 6.4.： |
| Bounded and periodic solutions / 7.： |
| A fixed point principle / 7.1.： |
| The use of majorant functions / 7.2.： |
| The Green function / 7.4.： |
| Comparison of Green functions / 7.5.： |
| The second Bogoljubov theorem / 7.6.： |
| Application of Darbo's fixed point principle / 7.7.： |
| Application of the Fredholm alternative / 7.8.： |
| A general approach / 8.： |
| Explicit solution for a particular class / 8.2.： |
| An abstract degeneration result / 8.3.： |
| Stationary boundary value problems / 9.： |
| The abstract problem / 9.1.： |
| Equivalent operator equations / 9.2.： |
| Reduction to a two-dimensional integral equation / 9.3.： |
| Application of K-normed spaces / 9.4.： |
| Unbounded multipliers / 9.5.： |
| Non-stationary boundary value problems / 10.： |
| Equations with variable operators / 10.1.： |
| Partial Integral Operators / 10.2.： |
| General properties / 11.： |
| Continuity properties / 11.1.： |
| Regularity properties / 11.2.： |
| The associate operator / 11.3.： |
| Algebras of partial integral operators / 11.4.： |
| Operators in spaces with mixed norm / 12.： |
| Ideal spaces with mixed norm / 12.1.： |
| Lebesgue spaces with mixed norm / 12.2.： |
| Orlicz spaces with mixed norm / 12.3.： |
| Operator functions with values in [characters not reproducible][subscript p](L[subscript [infinity]]) and [characters not reproducible][subscript p](L[subscript 1]) / 12.4.： |
| Operator functions with values in [characters not reproducible][subscript p](L[subscript p]) / 12.5.： |
| Partial integral operators in the space C / 13.： |
| Weakly continuous functions / 13.1.： |
| Acting and boundedness conditions / 13.2.： |
| Operator functions with values in [characters not reproducible][subscript p](C) / 13.3.： |
| Spectral properties / 14.： |
| Essential spectra of bounded linear operators / 14.1.： |
| Application to partial integral operators in L[subscript 2] / 14.2.： |
| Application to other partial integral operators / 14.3.： |
| An index formula for partial integral operators / 14.4.： |
| The case of positive kernels / 14.5.： |
| Linear partial integral equations / 15.： |
| Fredholm equations / 15.1.： |
| Volterra equations / 15.2.： |
| Bounded and continuous solutions / 15.3.： |
| Using tensor products / 15.4.： |
| Using eigenfunction expansions / 15.5.： |
| Generalizations and Applications / Chapter IV.： |
| Generalized equations of Barbashin type / 16.： |
| Reduction to partial integral equations / 16.1.： |
| Volterra operators and Barbashin equations / 16.2.： |
| Generalized Barbashin equations / 16.3.： |
| Nonlinear equations and operators / 16.4.： |
| Barbashin equations with Uryson operators / 17.1.： |
| Equations with Hammerstein operators / 17.2.： |
| Surjectivity results for monotone operators / 17.4.： |
| Equations with monotone operators / 17.5.： |
| Variational methods / 17.6.： |
| The Newton-Kantorovich method / 18.： |
| The abstract Newton-Kantorovich method / 18.1.： |
| Lipschitz conditions for derivatives / 18.2.： |
| Lipschitz conditions for partial Uryson operators / 18.3.： |
| The case X = C(T [times] S) / 18.4.： |
| The case X = L[subscript infinity] (T [times] S) / 18.5.： |
| The case X = L[subscript p](T [times] S) (1 [less than or equal] p [ [infinity]) / 18.6.： |
| Applications of Barbashin equations / 19.： |
| Applications to probability theory / 19.1.： |
| Applications to evolution equations / 19.2.： |
| Systems with substantially distributed parameters / 19.3.： |
| The Kimura continuum-of-alleles model / 19.4.： |
| An application to a radiation problem / 19.5.： |
| Applications to astrophysics / 19.6.： |
| Plane-parallel transport problems / 19.7.： |
| Applications of partial integral equations / 20.： |
| Applications to elasticity theory / 20.1.： |
| Applications to mechanics of continuous media / 20.2.： |
| Mixed problems of evolutionary type / 20.3.： |
| Axially symmetric contact problems / 20.4.： |
| Creeping of non-uniformly aging bodies / 20.5.： |
| A unified approach to some equations of mechanics / 20.6.： |
| Other applications / 20.7.： |
| References |
| List of symbols |
| Index |
| Preface |
| Introduction |
| Equations of Barbashin Type / Chapter I.： |
図書
