Article
| Title: | Boundary value problems with bounded $\varphi $-Laplacian and nonlocal conditions of integral type (English) |
| Author: | Bugajewska, Daria |
| Author: | Mawhin, Jean |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 277-288 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded $\varphi $-Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals. (English) |
| Keyword: | boundary value problem |
| Keyword: | $\varphi $-Laplacian |
| Keyword: | functions of bounded variation |
| Keyword: | Riemann-Stieltjes integral |
| Keyword: | prescribed curvature |
| MSC: | 34B10 |
| MSC: | 47H30 |
| DOI: | 10.21136/CMJ.2023.0154-23 |
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| Date available: | 2025-03-11T16:03:16Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152908 |
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| Reference: | [1] Appell, J., Bugajewska, D., Reinwand, S.: Nonlocal boundary value problems with BV- type data.Electron. J. Qual. Theory Differ. Equ. 2020 (2020), Article ID 69, 18 pages. Zbl 1474.34121, MR 4208476, 10.14232/ejqtde.2020.1.69 |
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| Reference: | [3] Bereanu, C., Mawhin, J.: Boundary-value problems with non-surjective $\phi$-Laplacian and one-sided bounded nonlinearity.Adv. Differ. Equ. 11 (2006), 35-60. Zbl 1111.34016, MR 2192414 |
| Reference: | [4] Bonheure, D., Habets, P., Obersnel, F., Omari, P.: Classical and non-classical positive solutions of a prescribed curvature equation with singularities.Rend. Ist. Mat. Univ. Trieste 39 (2007), 63-85. Zbl 1160.34015, MR 2441611 |
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| Reference: | [7] Infante, G., Webb, J. R. L.: Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations.Proc. Edinb. Math. Soc., II. Ser. 49 (2006), 637-656 \99999DOI99999 10.1017/S0013091505000532 . Zbl 1115.34026, MR 2266153, 10.1017/S0013091505000532 |
| Reference: | [8] Kusahara, T., Usami, H.: A barrier method for quasilinear ordinary differential equations of the curvature type.Czech. Math. J. 50 (2000), 185-196. Zbl 1046.34009, MR 1745471, 10.1023/A:1022409808258 |
| Reference: | [9] Leray, J., Schauder, J.: Topologie et équations fonctionnelles.Ann. Sci. Éc. Norm. Supér., III. Ser. 51 (1934), 45-78 French. Zbl 0009.07301, MR 1509338, 10.24033/asens.836 |
| Reference: | [10] Mawhin, J.: Topological Degree Methods in Nonlinear Boundary Value Problems.Regional Conference Series in Mathematics 40. AMS, Providence (1979). Zbl 0414.34025, MR 0525202, 10.1090/cbms/040 |
| Reference: | [11] Mawhin, J.: Boundary value problems for nonlinear perturbations of some $\phi$-Laplacians.Fixed Point Theory and its Applications Banach Center Publications 77. Institute of Mathematics, Polish Academy of Sciences, Warsaw (2007), 201-214. Zbl 1129.34010, MR 2338585, 10.4064/bc77-0-15 |
| Reference: | [12] Monteiro, G. A., Slavík, A., Tvrdý, M.: Kurzweil-Stieltjes Integral: Theory and Applications.Series in Real Analysis 15. World Scientific, Hackensack (2019). Zbl 1437.28001, MR 3839599, 10.1142/9432 |
| Reference: | [13] Webb, J. R. L.: Positive solutions of a boundary value problem with integral boundary conditions.Electron. J. Differ. Equ. 2011 (2011), Article ID 55, 10 pages. Zbl 1229.34039, MR 2801240 |
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