THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH LARGE OR QUICKLY CHANGING COEFFICIENTS AND BOUNDARY CONDITIONS

Abstract

CONTENTS Introduction Chapter One. Boundary-value problems with coefficients large in a subregion (problems with barriers) § 1. Statement of the problem. The regular case and the case of being on the spectrum § 2. Other problems with large coefficients Chapter Two. Boundary-value problems with infinitely narrow barriers § 3. Iteration process in the regular case and the case of coincidence with the spectrum § 4. Certain examples Chapter Three. Boundary-value problems with quickly oscillating boundary conditions § 5. Certain problems with constant coefficients § 6. General considerations and the elliptic case § 7. Nonstationary problems with quickly oscillating boundary conditions § 8. Equations containing a small parameter in the terms with higher order derivatives for quickly oscillating boundary conditions § 9. Eigenfunctions oscillating quickly on the boundary Appendix I. Generalised quickly oscillating boundary conditions Appendix II. Equations with quickly oscillating independent term Appendix III. Proof of Theorems 2 and 3 References