TY - JOUR

T1 - Weight summability of solutions of the Sturm-Liouville equation

AU - Chernyavskaya, N.

AU - Shuster, L.

N1 - Funding Information:
* Supported by the Israel Academy of sciences under Grant 431 95, -Supported by the Israel Academy of sciences under Grant 505 95.

PY - 1999/1/20

Y1 - 1999/1/20

N2 - We consider an equation -y″(x)+q(x)y(x)=f(x), x∈R; (1) where f(x)∈Lp(R), p∈[1,∞] (L∞(R):=C(R)), 1≤q(x)∈Lloc1(R). We study requirements for a weight function r(x)∈Llocp(R) and for q(x) under which, for a given p∈[1,∞], regardless of f(x)∈Lp(R), the solution y(x)∈Lp(R) of Eq. (1) satisfies the inequalities: r(x)y(x)p≤cf(x)p, y″(x)p+q(x)y(x)p≤c f(x)p, c=const.

AB - We consider an equation -y″(x)+q(x)y(x)=f(x), x∈R; (1) where f(x)∈Lp(R), p∈[1,∞] (L∞(R):=C(R)), 1≤q(x)∈Lloc1(R). We study requirements for a weight function r(x)∈Llocp(R) and for q(x) under which, for a given p∈[1,∞], regardless of f(x)∈Lp(R), the solution y(x)∈Lp(R) of Eq. (1) satisfies the inequalities: r(x)y(x)p≤cf(x)p, y″(x)p+q(x)y(x)p≤c f(x)p, c=const.

UR - http://www.scopus.com/inward/record.url?scp=0033585273&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1998.3517

DO - 10.1006/jdeq.1998.3517

M3 - Article

AN - SCOPUS:0033585273

VL - 151

SP - 456

EP - 473

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -