Toward General Theory of Differential-Operator and Kinetic Models (World Scientific Nonlinear Science Series a)

Foreword
Contents
Introduction
Acknowledgments
Part I Operator and Differential-Operator Equations
	1. Auxiliary Information on the Theory of Linear Operators
	2. Volterra Operator Equations with Piecewise Continuous Kernels: Solvability and Regularized Approximate Methods
	3. Nonlinear Differential Equations Near Branching Points
	4. Nonlinear Operator Equations with a Functional Perturbation of the Argument
	5. Nonlinear Systems’ Equilibrium Points: Stability, Branching, Blow-Up
	6. Nonclassic Boundary Value Problems in the Theory of Irregular Systems of Equations with Partial Derivatives
	7. Epilogue for Part I
Part II: Lyapunov Methods in Theory of Nonlinear Equations with Parameters
	8. Lyapunov Convex Majorants in the Existence Theorems
	9. Investigation of Bifurcation Points of Nonlinear Equations
	10. General Existence Theorems for the Bifurcation Points
	11. Construction of Asymptotics in a Neighborhood of a Bifurcation Point
	12. Regularization of Computation of Solutions in a Branch Point Neighborhood
	13. Iteration Methods, Analytical Initial Approximations, Interlaced Equations
	14. Iterative Methods Using Newton Diagrams
	15. Small Solutions of Nonlinear Equations with Vector
Parameter in Sectorial Neighborhoods
	16. Successive Approximations to the Solutions to Nonlinear Equations with a Vector Parameter
	17. Interlaced and Potential Branching Equation
	18 Epilogue for Part-II
Part III: Kinetic Models
	19. The Family of Steady-State Solutions of Vlasov–Maxwell System
	20. Boundary Value Problems for the Vlasov–Maxwell System
	21. Stationary Solutions of Vlasov–Maxwell System
	22. Existence of Solutions for the Boundary Value Problem
	23. Nonstationary Solutions of the Vlasov–Maxwell System
	24. Linear Stability of the Stationary Solutions of the Vlasov–Maxwell System
	25. Bifurcation of Stationary Solutions of the Vlasov–Maxwell System
	26. Statement of the Boundary Value Problem and the Bifurcation Problem
	27. Resolving Branching Equation
	28. Numerical Modeling of the Limit Problem for the Magnetically Noninsulated Diode
	29. Open Problems
Bibliography
Index