| Title:
|
Boundary value problems for the Schrödinger equation involving the Henstock-Kurzweil integral (English) |
| Author:
|
Sánchez-Perales, Salvador |
| Author:
|
Mendoza-Torres, Francisco J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
519-537 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation $-y''+qy=f$, where $q$ and $f$ are Henstock-Kurzweil integrable functions on $[a,b]$. Results presented in this article are generalizations of the classical results for the Lebesgue integral. (English) |
| Keyword:
|
Henstock-Kurzweil integral |
| Keyword:
|
Schrödinger operator |
| Keyword:
|
${\rm ACG}_{*}$-function |
| Keyword:
|
bounded variation function |
| MSC:
|
26A39 |
| MSC:
|
26A45 |
| MSC:
|
34B24 |
| idZBL:
|
07217149 |
| idMR:
|
MR4111857 |
| DOI:
|
10.21136/CMJ.2019.0388-18 |
| . |
| Date available:
|
2020-06-17T12:36:26Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148243 |
| . |
| Reference:
|
[1] Bartle, R. G.: A Modern Theory of Integration.Graduate Studies in Mathematics 32, AMS, Providence (2001). Zbl 0968.26001, MR 1817647, 10.1090/gsm/032 |
| Reference:
|
[2] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations.Universitext, Springer, New York (2011). Zbl 1220.46002, MR 2759829, 10.1007/978-0-387-70914-7 |
| Reference:
|
[3] Gordon, R. A.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock.Graduate Studies in Mathematics 4, AMS, Providence (1994). Zbl 0807.26004, MR 1288751, 10.1090/gsm/004 |
| Reference:
|
[4] Peral, I.: Primer Curso de Ecuaciones en Derivadas Parciales.Addison Wesley, Boston (1995), Spanish. |
| Reference:
|
[5] Sánchez-Perales, S.: The initial value problem for the Schrödinger equation involving the Henstock-Kurzweil integral.Rev. Unión Mat. Argent. 58 (2017), 297-306. Zbl 1382.34096, MR 3733209 |
| Reference:
|
[6] Swartz, C.: Norm convergence and uniform integrability for the Henstock-Kurzweil integral.Real Anal. Exch. 24 (1998), 423-426. Zbl 0943.26022, MR 1691761, 10.2307/44152964 |
| Reference:
|
[7] Talvila, E.: Henstock-Kurzweil Fourier transforms.Ill. J. Math. 46 (2002), 1207-1226. Zbl 1037.42007, MR 1988259, 10.1215/ijm/1258138475 |
| . |
