Boundary value problems with bounded ϕ -Laplacian and nonlocal conditions of integral type

Daria Bugajewska; Jean Mawhin

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 277-288
  • ISSN: 0011-4642

Abstract

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We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded ϕ -Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.

How to cite

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Bugajewska, Daria, and Mawhin, Jean. "Boundary value problems with bounded $\varphi $-Laplacian and nonlocal conditions of integral type." Czechoslovak Mathematical Journal (2025): 277-288. <http://eudml.org/doc/299919>.

@article{Bugajewska2025,
abstract = {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.},
author = {Bugajewska, Daria, Mawhin, Jean},
journal = {Czechoslovak Mathematical Journal},
keywords = {boundary value problem; $\varphi $-Laplacian; functions of bounded variation; Riemann-Stieltjes integral; prescribed curvature},
language = {eng},
number = {1},
pages = {277-288},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundary value problems with bounded $\varphi $-Laplacian and nonlocal conditions of integral type},
url = {http://eudml.org/doc/299919},
year = {2025},
}

TY - JOUR
AU - Bugajewska, Daria
AU - Mawhin, Jean
TI - Boundary value problems with bounded $\varphi $-Laplacian and nonlocal conditions of integral type
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 277
EP - 288
AB - 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.
LA - eng
KW - boundary value problem; $\varphi $-Laplacian; functions of bounded variation; Riemann-Stieltjes integral; prescribed curvature
UR - http://eudml.org/doc/299919
ER -

References

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  1. Appell, J., Bugajewska, D., Reinwand, S., 10.14232/ejqtde.2020.1.69, Electron. J. Qual. Theory Differ. Equ. 2020 (2020), Article ID 69, 18 pages. (2020) Zbl1474.34121MR4208476DOI10.14232/ejqtde.2020.1.69
  2. Bereanu, C., Mawhin, J., Nonlinear Neumann boundary value problems with φ -Laplacian operators, An. Ştiinţ. Univ. Ovidus Constanţa, Ser. Mat. 12 (2004), 73-82. (2004) Zbl1117.34015MR2209116
  3. Bereanu, C., Mawhin, J., Boundary-value problems with non-surjective φ -Laplacian and one-sided bounded nonlinearity, Adv. Differ. Equ. 11 (2006), 35-60. (2006) Zbl1111.34016MR2192414
  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. (2007) Zbl1160.34015MR2441611
  5. Bugajewska, D., Infante, G., Kasprzak, P., 10.4171/zaa/1594, Z. Anal. Anwend. 36 (2017), 393-417. (2017) Zbl1384.45005MR3713050DOI10.4171/zaa/1594
  6. Habets, P., Omari, P., 10.1142/S0219199707002617, Commun. Contemp. Math. 9 (2007), 701-730. (2007) Zbl1153.34015MR2361738DOI10.1142/S0219199707002617
  7. Infante, G., Webb, J. R. L., 10.1017/S0013091505000532, Proc. Edinb. Math. Soc., II. Ser. 49 (2006), 637-656 9999DOI99999 10.1017/S0013091505000532 . (2006) Zbl1115.34026MR2266153DOI10.1017/S0013091505000532
  8. Kusahara, T., Usami, H., 10.1023/A:1022409808258, Czech. Math. J. 50 (2000), 185-196. (2000) Zbl1046.34009MR1745471DOI10.1023/A:1022409808258
  9. Leray, J., Schauder, J., 10.24033/asens.836, Ann. Sci. Éc. Norm. Supér., III. Ser. 51 (1934), 45-78 French. (1934) Zbl0009.07301MR1509338DOI10.24033/asens.836
  10. Mawhin, J., 10.1090/cbms/040, Regional Conference Series in Mathematics 40. AMS, Providence (1979). (1979) Zbl0414.34025MR0525202DOI10.1090/cbms/040
  11. Mawhin, J., 10.4064/bc77-0-15, Fixed Point Theory and its Applications Banach Center Publications 77. Institute of Mathematics, Polish Academy of Sciences, Warsaw (2007), 201-214. (2007) Zbl1129.34010MR2338585DOI10.4064/bc77-0-15
  12. Monteiro, G. A., Slavík, A., Tvrdý, M., 10.1142/9432, Series in Real Analysis 15. World Scientific, Hackensack (2019). (2019) Zbl1437.28001MR3839599DOI10.1142/9432
  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. (2011) Zbl1229.34039MR2801240

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