TY - JOUR

T1 - A criterion for compactness in Lp (R) of the resolvent of the maximal general form Sturm-Liouville operator

AU - Chernyavskaya, N. A.

AU - Shuster, L. A.

N1 - Publisher Copyright:
© 2016 Royal Society of Edinburgh.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We consider the equation where and We assume that this equation is correctly solvable in Lp (R). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm-Liouville operator. Here In the case p = 2, for the compact operator, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.

AB - We consider the equation where and We assume that this equation is correctly solvable in Lp (R). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm-Liouville operator. Here In the case p = 2, for the compact operator, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.

KW - Sturm-Liouville operator

KW - compactness of resolvent

KW - estimates of minimal eigenvalues

UR - http://www.scopus.com/inward/record.url?scp=84964344273&partnerID=8YFLogxK

U2 - 10.1017/S0308210515000694

DO - 10.1017/S0308210515000694

M3 - Article

AN - SCOPUS:84964344273

VL - 146

SP - 483

EP - 508

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 3

ER -