TY - JOUR
T1 - Necessary and sufficient conditions for the solvability of a singular Dirichlet boundary problem for the Sturm-Liouville equation of general form
AU - Chernyavskaya, N.
AU - Shuster, L.
N1 - Publisher Copyright:
© 2024 Elsevier Inc.
PY - 2025/1/25
Y1 - 2025/1/25
N2 - We consider the boundary problem −(r(x)y′(x))′+q(x)y(x)=f(x),x∈R, lim|x|→∞y(x)=0 under the following conditions: 1) r>0,[Formula presented]∈L1loc(R),q∈L1loc(R); 2) equation (1) is correctly solvable in Lp(R), p∈(1,∞). We obtain necessary and sufficient requirements for the functions r and q under which, regardless of the choice of a function f∈Lp(R), p∈(1,∞), the solution y∈Lp(R) of equation (1) satisfies (2).
AB - We consider the boundary problem −(r(x)y′(x))′+q(x)y(x)=f(x),x∈R, lim|x|→∞y(x)=0 under the following conditions: 1) r>0,[Formula presented]∈L1loc(R),q∈L1loc(R); 2) equation (1) is correctly solvable in Lp(R), p∈(1,∞). We obtain necessary and sufficient requirements for the functions r and q under which, regardless of the choice of a function f∈Lp(R), p∈(1,∞), the solution y∈Lp(R) of equation (1) satisfies (2).
KW - Dirichlet problem
KW - General Sturm-Liouville equation
UR - http://www.scopus.com/inward/record.url?scp=85208074421&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2024.10.023
DO - 10.1016/j.jde.2024.10.023
M3 - Article
AN - SCOPUS:85208074421
SN - 0022-0396
VL - 416
SP - 1564
EP - 1601
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -