INTRODUCTION . . . . . . xiii Β§ 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 Β§ 2. EQUATIONS WITH A CLOSED OPERATOR 6 Β§ 3. THE ADJOINT EQUATION . . . . . . 10 Β§ 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 Β§ 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 Β§ 6. A PRIORI ESTIMATES .. . . . . . 24 Β§ 7. EQUATIONS WITH FINITE DEFECT . . . 27 Β§ 8. Β§ 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 Β§ 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 Β§ 11. Β§ 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 Β§ 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 Β§ 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 Β§ 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 Β§ 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 Β§ 17. Β§ 18. UNDETERMINED EQUATIONS 62 Β§ 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 Β§ 20. APPENDIX. BASIC RESULTS FROM FUNCTIONAL ANALYSIS USED IN THE TEXT 95 LITERATURE CITED . . . . . . . . . . . . . . . . . . .. . . . 99 . . PRE F ACE The basic material appearing in this book represents the substance v of a special series of lectures given by the author at Voronez University in 1968/69, and, in part, at Dagestan University in 1970.