TY - JOUR
T1 - Correct Solvability, Embedding Theorems and Separability for the Sturm-Liouville Equation
AU - Chernyavskaya, N.A.
AU - Shuster, L.
PY - 2013
Y1 - 2013
N2 - We consider the equation - y"(x)+q(x)y(x)=f(x), x\in R and the weighted function space S_p^{(2)}(R,q)=\{y\in AC_{\loc}^{(1)}(R):\|y"-qy\|_p+\|q^{1/p}y\|_p<\infty\}; p\in[1,\infty), f\in L_p(R)and0\le q\in L_1^{\loc}(R).WeshowthatthereexistsanembeddingS(2)p(R,q)↪Lp(R)ifandonlyifequationaboveiscorrectlysolvableinL_p(R).
AB - We consider the equation - y"(x)+q(x)y(x)=f(x), x\in R and the weighted function space S_p^{(2)}(R,q)=\{y\in AC_{\loc}^{(1)}(R):\|y"-qy\|_p+\|q^{1/p}y\|_p<\infty\}; p\in[1,\infty), f\in L_p(R)and0\le q\in L_1^{\loc}(R).WeshowthatthereexistsanembeddingS(2)p(R,q)↪Lp(R)ifandonlyifequationaboveiscorrectlysolvableinL_p(R).
UR - http://arxiv.org/abs/1307.5611
M3 - Article
VL - 8
SP - 45
EP - 52
JO - Bollettino della Unione Matematica Italiana
JF - Bollettino della Unione Matematica Italiana
IS - 1
ER -