TY - JOUR
T1 - A criterion for correct solvability of the Sturm-Liouville equation in the space Lp(R)
AU - Chernyavskaya, N.
AU - Shuster, L.
PY - 2002
Y1 - 2002
N2 - We consider an equation (1) - y″(x) + q(x) y(x) = f(x), x ∈ R, where f(x) ∈ Lp(R), p ∈ [1, ∞] (||f||∞ := C(R)), and 0 ≤ q(x) ∈ L1loc(R). By a solution of equation (1), we mean any function y(x) such that y(x), y′(x) ∈ ACloc(R), and equality (1) holds almost everywhere on R. In this paper, we obtain a criterion for the correct solvability of (1) in Lp(R), p ∈ [1, ∞].
AB - We consider an equation (1) - y″(x) + q(x) y(x) = f(x), x ∈ R, where f(x) ∈ Lp(R), p ∈ [1, ∞] (||f||∞ := C(R)), and 0 ≤ q(x) ∈ L1loc(R). By a solution of equation (1), we mean any function y(x) such that y(x), y′(x) ∈ ACloc(R), and equality (1) holds almost everywhere on R. In this paper, we obtain a criterion for the correct solvability of (1) in Lp(R), p ∈ [1, ∞].
KW - Correct solvability
KW - Sturm-Liouville equation
UR - http://www.scopus.com/inward/record.url?scp=0035994133&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-01-06145-7
DO - 10.1090/S0002-9939-01-06145-7
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AN - SCOPUS:0035994133
SN - 0002-9939
VL - 130
SP - 1043
EP - 1054
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -