TY - JOUR
T1 - Criteria for correct solvability of a general Sturm–Liouville equation in the space L1(R)
AU - Chernyavskaya, N.
AU - Shuster, L.
N1 - Publisher Copyright:
© 2017, Unione Matematica Italiana.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - We consider the equation -(r(x)y′(x))′+q(x)y(x)=f(x),x∈Rwhere f∈ L1(R) and r>0,q≥0,1/r∈L1loc(R),q∈L1loc(R),lim|d|→∞∫x-dxdtr(t)·∫x-dxq(t)dt=∞.By a solution of (1), we mean any function y, absolutely continuous in R together with ry′, which satisfies (1) almost everywhere in R. Under conditions (2) and (3), we give a criterion for correct solvability of (1) in the space L1(R).
AB - We consider the equation -(r(x)y′(x))′+q(x)y(x)=f(x),x∈Rwhere f∈ L1(R) and r>0,q≥0,1/r∈L1loc(R),q∈L1loc(R),lim|d|→∞∫x-dxdtr(t)·∫x-dxq(t)dt=∞.By a solution of (1), we mean any function y, absolutely continuous in R together with ry′, which satisfies (1) almost everywhere in R. Under conditions (2) and (3), we give a criterion for correct solvability of (1) in the space L1(R).
UR - http://www.scopus.com/inward/record.url?scp=85035793174&partnerID=8YFLogxK
U2 - 10.1007/s40574-017-0144-y
DO - 10.1007/s40574-017-0144-y
M3 - Article
AN - SCOPUS:85035793174
SN - 1972-6724
VL - 11
SP - 417
EP - 443
JO - Bolletino dell Unione Matematica Italiana
JF - Bolletino dell Unione Matematica Italiana
IS - 4
ER -