TY - JOUR
T1 - An embedding theorem for a weighted space of Sobolev type and correct solvability of the Sturm-Liouville equation
AU - Chernyavskaya, Nina A.
AU - Shuster, Leonid A.
PY - 2012/9
Y1 - 2012/9
N2 - We consider the weighted space W 1 (2)(ℝ,q) of Sobolev type Here f ε L 1(ℝ) and 0 ≥ q ∈ L 1 loc(ℝ). We prove the following:The problems of embedding W 1 (2)(ℝq) {right arrow, hooked} L 1(ℝ) and of correct solvability of (1) in L 1(ℝ) are equivalent an embedding W 1 (2)(ℝ,q) {right arrow, hooked} L 1(ℝ) exists if and only if.
AB - We consider the weighted space W 1 (2)(ℝ,q) of Sobolev type Here f ε L 1(ℝ) and 0 ≥ q ∈ L 1 loc(ℝ). We prove the following:The problems of embedding W 1 (2)(ℝq) {right arrow, hooked} L 1(ℝ) and of correct solvability of (1) in L 1(ℝ) are equivalent an embedding W 1 (2)(ℝ,q) {right arrow, hooked} L 1(ℝ) exists if and only if.
KW - Sobolev space
KW - Sturm-Liouville equation
KW - embedding theorem
UR - http://www.scopus.com/inward/record.url?scp=84867686919&partnerID=8YFLogxK
U2 - 10.1007/s10587-012-0041-6
DO - 10.1007/s10587-012-0041-6
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AN - SCOPUS:84867686919
SN - 0011-4642
VL - 62
SP - 709
EP - 716
JO - Czechoslovak Mathematical Journal
JF - Czechoslovak Mathematical Journal
IS - 3
ER -