SOME PROBLEMS OF THE QUALITATIVE THEORY OF SECOND ORDER ELLIPTIC EQUATIONS (CASE OF SEVERAL INDEPENDENT VARIABLES)
E. M. Landis · Russian Mathematical Surveys · 1963
CONTENTSIntroductionChapter I. Properties of solutions with constant sign § 0. Introduction § 1. Conditions placed on the coefficients of the equation. Some notations § 2. Continuation of a quadratic form from a domain to the whole space § 3. The principal lemma § 4. Character of growth of a solution in a bounded domain § 5. Theorem of Phragmen-Lindelof type § 6. Growth and decay of the solution at infinity and in the neighbourhood of a boundary point § 7. The principal lemma for the self-adjoint equation § 8. A theorem of analysis § 9. Theorems on the growth and decay of a positive solution of a self-adjoint equationChapter II. Properties of solutions with changing sign § 0. Introduction § 1. The uniqueness theorem § 2. Three-sphere theorem § 3. On the admissible rate of decay of the solution in a semicylinder § 4. The relation between the number of changes of sign of the solution and its growthList of references