Green-Liouville approximation and correct solvability in of the general Sturm-Liouville equation
Nina Chernyavskaya; Leonid Shuster
Czechoslovak Mathematical Journal (2024)
- Issue: 1, page 247-272
- ISSN: 0011-4642
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topChernyavskaya, Nina, and Shuster, Leonid. "Green-Liouville approximation and correct solvability in $L_p(\mathbb {R})$ of the general Sturm-Liouville equation." Czechoslovak Mathematical Journal (2024): 247-272. <http://eudml.org/doc/299223>.
@article{Chernyavskaya2024,
abstract = {We consider the equation \[ -(r(x) y^\{\prime \}(x))^\{\prime \}+q(x)y(x)=f(x),\quad x\in \mathbb \{R\}, \]
where $f\in L_p(\mathbb \{R\})$, $p\in (1,\infty )$ and \[ r>0,\quad \frac\{1\}\{r\}\in L\_1^\{\rm loc\}(\mathbb \{R\}),\quad q\in L\_1^\{\rm loc\}(\mathbb \{R\}). \]
For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions $r$ and $q$ under which the above equation is correctly solvable in the space $L_p(\mathbb \{R\}),$$p\in (1,\infty ).$},
author = {Chernyavskaya, Nina, Shuster, Leonid},
journal = {Czechoslovak Mathematical Journal},
keywords = {Green-Liouville approximation; correct solvability; general Sturm-Liouville equation},
language = {eng},
number = {1},
pages = {247-272},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Green-Liouville approximation and correct solvability in $L_p(\mathbb \{R\})$ of the general Sturm-Liouville equation},
url = {http://eudml.org/doc/299223},
year = {2024},
}
TY - JOUR
AU - Chernyavskaya, Nina
AU - Shuster, Leonid
TI - Green-Liouville approximation and correct solvability in $L_p(\mathbb {R})$ of the general Sturm-Liouville equation
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 247
EP - 272
AB - We consider the equation \[ -(r(x) y^{\prime }(x))^{\prime }+q(x)y(x)=f(x),\quad x\in \mathbb {R}, \]
where $f\in L_p(\mathbb {R})$, $p\in (1,\infty )$ and \[ r>0,\quad \frac{1}{r}\in L_1^{\rm loc}(\mathbb {R}),\quad q\in L_1^{\rm loc}(\mathbb {R}). \]
For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions $r$ and $q$ under which the above equation is correctly solvable in the space $L_p(\mathbb {R}),$$p\in (1,\infty ).$
LA - eng
KW - Green-Liouville approximation; correct solvability; general Sturm-Liouville equation
UR - http://eudml.org/doc/299223
ER -
References
top- Chernyavskaya, N. A., Shuster, L. A., On the WKB-method, Differ. Uravn. 25 (1989), 1826-1829 Russian. (1989) Zbl0702.34053MR1025660
- Chernyavskaya, N., Shuster, L., 10.1090/S0002-9939-97-04186-5, Proc. Am. Math. Soc. 125 (1997), 3213-3228. (1997) Zbl0884.34063MR1443146DOI10.1090/S0002-9939-97-04186-5
- Chernyavskaya, N., Shuster, L., 10.1090/S0002-9939-99-05049-2, Proc. Am. Math. Soc. 127 (1999), 1413-1426. (1999) Zbl0918.34032MR1625725DOI10.1090/S0002-9939-99-05049-2
- Chernyavskaya, N., Shuster, L., 10.4310/MAA.2000.v7.n1.a4, Methods Appl. Anal. 7 (2000), 65-84. (2000) Zbl0985.34019MR1796006DOI10.4310/MAA.2000.v7.n1.a4
- Chernyavskaya, N., Shuster, L., 10.1090/S0002-9939-01-06145-7, Proc. Am. Math. Soc. 130 (2002), 1043-1054. (2002) Zbl0994.34014MR1873778DOI10.1090/S0002-9939-01-06145-7
- Chernyavskaya, N. A., Shuster, L. A., 10.4171/ZAA/1285, Z. Anal. Anwend. 25 (2006), 205-235. (2006) Zbl1122.34021MR2229446DOI10.4171/ZAA/1285
- Chernyavskaya, N., Shuster, L., 10.1112/jlms/jdp012, J. Lond. Math. Soc., II. Ser. 80 (2009), 99-120. (2009) Zbl1188.34036MR2520380DOI10.1112/jlms/jdp012
- Chernyavskaya, N. A., Shuster, L. A., 10.1007/s10587-014-0154-1, Czech. Math. J. 64 (2014), 1067-1098. (2014) Zbl1349.34093MR3304799DOI10.1007/s10587-014-0154-1
- Chernyavskaya, N., Shuster, L., 10.1007/s40574-017-0144-y, Boll. Unione Mat. Ital. 11 (2018), 417-443. (2018) Zbl1404.34019MR3869579DOI10.1007/s40574-017-0144-y
- Chernyavskaya, N., Shuster, L., 10.48550/arXiv.2210.02911, Available at https://arxiv.org/abs/2210.02911 (2022), 29 pages. (2022) MR3376914DOI10.48550/arXiv.2210.02911
- Davies, E. B., Harrell, E. M., 10.1016/0022-0396(87)90030-1, J. Differ. Equations 66 (1987), 165-188. (1987) Zbl0616.34020MR0871993DOI10.1016/0022-0396(87)90030-1
- Hartman, P., Ordinary Differential Equations, John Wiley & Sons, New York (1964). (1964) Zbl0125.32102MR0171038
- Mynbaev, K. T., Otelbaev, M. O., Weighted Functional Spaces and the Spectrum of Differential Operators, Nauka, Moscow (1988), Russian. (1988) Zbl0651.46037MR0950172
- Olver, F. W. J., 10.1016/c2013-0-11254-8, Academic Press, New York (1974). (1974) Zbl0303.41035MR0435697DOI10.1016/c2013-0-11254-8
- Titchmarsh, E. C., The Theory of Functions, Oxford University Press, Oxford (1932). (1932) Zbl0005.21004MR3728294
- Whittaker, E. T., Watson, G. N., 10.1017/CBO9780511608759, Cambridge University Press, Cambridge (1962). (1962) Zbl0105.26901MR0178117DOI10.1017/CBO9780511608759
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