Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
boundary value problem; $\varphi $-Laplacian; functions of bounded variation; Riemann-Stieltjes integral; prescribed curvature
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.
References:
[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. DOI 10.14232/ejqtde.2020.1.69 | MR 4208476 | Zbl 1474.34121
[2] Bereanu, C., Mawhin, J.: Nonlinear Neumann boundary value problems with $\phi$-Laplacian operators. An. Ştiinţ. Univ. Ovidus Constanţa, Ser. Mat. 12 (2004), 73-82. MR 2209116 | Zbl 1117.34015
[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. MR 2192414 | Zbl 1111.34016
[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. MR 2441611 | Zbl 1160.34015
[5] Bugajewska, D., Infante, G., Kasprzak, P.: Solvability of Hammerstein integral equations with applications to boundary value problems. Z. Anal. Anwend. 36 (2017), 393-417. DOI 10.4171/zaa/1594 | MR 3713050 | Zbl 1384.45005
[6] Habets, P., Omari, P.: Multiple positive solutions of a one-dimensional prescribed mean curvature problem. Commun. Contemp. Math. 9 (2007), 701-730. DOI 10.1142/S0219199707002617 | MR 2361738 | Zbl 1153.34015
[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 . DOI 10.1017/S0013091505000532 | MR 2266153 | Zbl 1115.34026
[8] Kusahara, T., Usami, H.: A barrier method for quasilinear ordinary differential equations of the curvature type. Czech. Math. J. 50 (2000), 185-196. DOI 10.1023/A:1022409808258 | MR 1745471 | Zbl 1046.34009
[9] Leray, J., Schauder, J.: Topologie et équations fonctionnelles. Ann. Sci. Éc. Norm. Supér., III. Ser. 51 (1934), 45-78 French. DOI 10.24033/asens.836 | MR 1509338 | Zbl 0009.07301
[10] Mawhin, J.: Topological Degree Methods in Nonlinear Boundary Value Problems. Regional Conference Series in Mathematics 40. AMS, Providence (1979). DOI 10.1090/cbms/040 | MR 0525202 | Zbl 0414.34025
[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. DOI 10.4064/bc77-0-15 | MR 2338585 | Zbl 1129.34010
[12] Monteiro, G. A., Slavík, A., Tvrdý, M.: Kurzweil-Stieltjes Integral: Theory and Applications. Series in Real Analysis 15. World Scientific, Hackensack (2019). DOI 10.1142/9432 | MR 3839599 | Zbl 1437.28001
[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. MR 2801240 | Zbl 1229.34039
Partner of
EuDML logo