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Differential Equations

Proceedings of the 1987 Equadiff Conference

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## Book Description

This volume is an outcome of the EQUADIFF 87 conference in Greece. It addresses a wide spectrum of topics in the theory and applications of differential equations, ordinary, partial, and functional. The book is intended for mathematics and scientists.

## Table of Contents

1. On the Jabotinsky Equations 2. Global Decoupling of Coupled Symmetric Oscillators 3. Void Formation in Solidification 4. Forced Oscillations for Hamiltonian Systems 5. Eigenvalues, Bifurcation, and Center Manifolds in the Presence of Noise 6. An Unusual Wave Equation Arising in Water-Wave Theory 7. Controllability and Approximate Controllability for Linear Integral Volterra-Stieltjes Equations 8. Determinants for Formally Hyperbolic Differential Equations 9. On Two New Applications of Gurtin's Coordinate Transformation 10. On the Thermal Stability of a Chemically Reacting Gas in a Porous Sphere 11. Higher Regularity of Solutions of Semilinear Evolution Equations and Applications 12. The Maximal Attractor of the Scalar Reaction Diffusion Equation 13. Stability of Bifurcating Solutions of Reaction-Diffusion Equations in Cylindrical Domains 14. Numerical Evaluation of the Solutions to the Equations of Elastostatics for a Stratified Sphere 15. Existence of Positive Exponentially Decreasing Solutions for Nonlinear Differential Equations in R with an Unbounded Coefficient 16. A Shadowing Lemma for Maps in Infinite Dimensions 17. Asymptotic Method for Invariant Solutions of Rm Maps 18. Orthogonal Polynomials in Symmetrical Domains of Rm 19. Hyperbolic Conservation Laws with Memory 20. Fully Nonlinear Equations in Banach Spaces 21. On the Number of Solutions of Some Semilinear Boundary Value Problems 22. Some Nonlinear Sturmian Theory for (|u'|p-2 u' )' + c(t)|u|p-2u=0 23. A Very Short Survey of Non Standard Analysis' Contribution to the Theory of Ordinary Differential Equations 24. A New Approach to Inverse Problems in Linear Kinetic Theory 25. Bounded Entire Solutions of Higher Order Semilinear Equations 26. Minors of the Wronskian of the Differential Equation Lny + p(x)y = 0 and Their Applications 27. Explicit Solutions of the Fokker-Planck Equation 28. Full and Half-Range Eigenfunction Expansions for an Elliptic Boundary Value Problem Involving an Indefinite Weight 29. The General Similarity Solution of Laplace's Equation with Applications to Boundary-Value Problems 30. Uniform Asymptotic Stability in Functional Differential Equations 31. Removability of Blowup Points for Semilinear Heat Equations 32. Behavior of the Nonoscillatory Solutions of First Order Neutral Delay Differential Equations 33. Some Stability-Type Results for Second Order Nonlinear Differential Equations 34. Optimal Control and Integral Equations 35. Oscillation of Neutral Delay Differential Equations Arising in Population Dynamics 36. Shadow Systems for Evolutionary Equations 37. On Periodic-Parabolic Boundary Value Problems 38. Periodic Solutions of a Linear Volterra System 39. On Multiple Periodic Solutions for Semilinear Wave Equations with Forcing Terms 40. Explicit Solutions for Riccati Operator Differential Equations 41. On Differential Inclusions of Second Order 42. Continuous Symmetrization and Related Problems 43. Lyapunov Stability and Attractors Under Discretization 44. A Method for Approximate Construction of Solution of First Order Differential Equations 45. An Existence Theorem for Nonlinear Random Differential Inclusions 46. Linearized Oscillations for Neutral Equations 47. Existence Theorems for Second Order Differential Equations with Piecewise Constant Argument 48. Oscillations of Second Order Neutral Equations 49. Monotonicity Results and Inequalities for the Zeros of Generalized Airy Functions 50. Asymptotic Behavior of Solutions to Quasilinear Schrodinger Equations 51. The Vibrations of a "Fractal Drum" 52. A Numerical Approach to the Dynamic Nonconvex Unilateral Problem of Soil-Pile Interaction 53. General Theory of Regular Solutions and Hyposolutions of the Homogeneous Equation du/dt = Au 54. Numerical Aspects of Waveform Relaxation 55. Asymptotics of Solutions of the Equation y" = f(g(x))ф(ψ(y)) 56. A Result of Homogenisation for a Viscoelastic Equation with Non-Periodic Coefficients 57. Exterior Stationary Problems for the Equations of Motion of Compressible Viscous and Heat-Conductive Fluids 58. On Boundary Value Problems for ODE with Parameters 59. Continuous Orthonormalization with Application to Burgers' Equation 60. Diffusion Equations as Singular Limits of Damped Wave Equations 61. Some Properties of Phase Spaces for Functional Differential Equations with Infinite Delay 62. Qualitative Behaviour of the Solutions of the Hamiltonian Systems H(r,θ,pr,pθ) = p2r/2 + p2θ/2r2 + V(r,θ), V(r,θ) = -ar-n(μcos2θ+sin2θ)-n/2, μ ε [1,∞], a εIR+, n ε IR+\{2}, Part One: Case nε (2,+∞) 63. Qualitative Behaviour of the Solutions of the Hamiltonian Systems H(r,θ,pr,pθ) = p2r/2 + p2θ/2r2 + V(r,θ), V(r,θ) = -ar-n(μcos2θ+sin2θ)-n/2, μ ε [1,∞], a εIR+, n ε IR+\{2}, Part Two: Case nε (0,2) 64. Semiperiodic Boundary Value Problems 65. Nonlinear Variational Eigenvalue Inclusions 66. On Minimal Realizations of Integral Operators with Semi-Separable Kernels 67. Elliptic Equations with Nearly Critical Growth 68. A Preliminary Model for the Cracking of Shrinking Crusts Sliding with Friction 69. Nonlocal Regularization of Some Overdetermined Boundary Value Problems 70. Nine-Point Finite-Difference Scheme for Solving Elliptic' Equations with Application in Capillary Instability of Viscous Jet in Inviscid Medium 71. Identification of a Non-Linear, Stochastic, and Integral Equation 72. On the Continuous Dependence for the Capillarity Problem with Obstacle 73. Operational Fractional Calculus of Kratzel Integral Transformation 74. Geometrical Structure of Attractors of Slow-Fast Dynamical Systems: The Double Scroll Chaotic Oscillator 75. The Exterior Nonstationary Problem for the Navier-Stokes Equations in Regions with Moving Boundaries 76. Monotonicity Properties of Solutions to Systems of Differential Equations Arising in Chemical Kinetics 77. On a Nonstationary Motion of a Finite Mass of a Liquid Bounded by a Free Surface 78. Realization of Transfer Functions by Equations of Parabolic Type 79. On the Converse of a Theorem of Milloux, Prodi, and Trevisan 80. Uniqueness of Solutions for Problems Arising in Population Genetics 81. Generalized Solutions of Mixed Problems for Quasilinear Hyperbolic Systems of Functional Partial Differential Equations 82. On the First Fourier Problem for Some Integro-Differential Equation of Parabolic Type 83. Invariant Regions for a Hyperbolic Version of the FitzHugh-Nagumo Equation 84. An Existence Theorem for Non-Homogeneous Inviscid Incompressible Fluids 85. A Small Concentration Expansion for the Effective Heat Conductivity of a Random Disperse Two-Component Material: An Assessment of Batchelor's Renormalization Method 86. Secondary Bifurcations in Symmetric Systems 87. On Controllability of Fisher's Model of Selection 88. The Small Dispersion Limit of the Korteweg-de Vries Equation 89. Analytic Semigroups Generated in C -1,α, by Second Order Variational Operators and Application to Nonlinear Cauchy Problem 90. Bifurcation of a Class of Partial Differential Equation Systems 91. Uber die Differentialgleichung y'' = f(x,y) 92. Stability of Nonlinear Stochastic Systems 93. Some Problems in Stability of the Equilibrium Related to Coexistence of Solutions to Hill's Equations