New upper estimate for positive solutions to a second order boundary value problem with a parameter
-
Liancheng Wang
lwang5@kennesaw.edu
-
Bo Yang
byang@kennesaw.edu
Downloads
DOI:
https://doi.org/10.56754/0719-0646.2501.121Abstract
We consider a second order boundary value problem with a parameter. A new upper bound for positive solutions and Green’s function of the problem is obtained.
Keywords
Mathematics Subject Classification:
Z. Bai, “Positive solutions of some nonlocal fourth-order boundary value problem”, Appl. Math. Comput., vol. 215, no. 12, pp. 4191–4197, 2010.
G. Chai, “Existence of positive solutions for second-order boundary value problem with one parameter”, J. Math. Anal. Appl., vol. 330, no. 1, pp. 541–549, 2007.
Y. Cui, “Multiple solutions to fourth-order boundary value problems”, Comput. Math. Appl., vol. 57, no. 4, pp. 643–649, 2009.
X. Dong and Z. Bai, “Positive solutions of fourth-order boundary value problem with variable parameters”, J. Nonlinear Sci. Appl., vol. 1, no. 1, pp. 21–30, 2008.
Y. Li, “Positive solutions of fourth-order boundary value problems with two parameters”, J. Math. Anal. Appl., vol. 281, no. 2, pp. 477–484, 2003.
Y. Li, “Positive solutions of fourth-order periodic boundary value problems”, Nonlinear Anal., vol. 54, no. 6, pp. 1069–1078, 2003.
X. Liu and W. Li, “Positive solutions of the nonlinear fourth-order beam equation with three parameters”, J. Math. Anal. Appl., vol. 303, no. 1, pp. 150–163, 2005.
R. Ma, “Nodal solutions for a fourth-order two-point boundary value problem”, J. Math. Anal. Appl., vol. 314, no. 1, pp. 254–265, 2006.
W. Shen and T. He, “Bifurcation from interval and positive solutions for a class of fourth- order two-point boundary value problem”, Bound. Value Probl., vol. 2013, Paper No. 170, 12 pages, 2013.
J. R. L. Webb and M. Zima, “Multiple positive solutions of resonant and non-resonant non- local fourth-order boundary value problems”, Glasg. Math. J., vol. 54, no. 1, pp. 225–240, 2012.
Z. L. Wei and C. C. Pang, “Positive solutions and multiplicity of fourth-order m-point boundary value problem with two parameters”, Nonlinear Anal., vol. 67, no. 5, pp. 1586–1598, 2007.
J. Xu and Z. Wei, “Positive solutions for multipoint boundary-value problem with parameters”, Electron. J. Differential Equations, vol. 2008, Paper No. 106, 8 pages, 2008.
B. Yang, “Upper and lower estimates for positive solutions of the higher order Lidstone boundary value problem”, J. Math. Anal. Appl., vol. 382, no. 1, pp. 290–302, 2011.
B. Yang, “Maximum principle for a fourth order boundary value problem”, Differ. Equ. Appl., vol. 9, no. 4, pp. 495–504, 2017.
B. Yang, “Positive solutions to a boundary value problem for the beam equation”, Z. Anal. Anwend., vol. 26, no. 2, pp. 221–230, 2007.
B. Yang, “Estimates of positive solutions to a boundary value problem for the beam equation”, Commun. Math. Anal., vol. 2, no. 1, pp. 13–21, 2007.
Similar Articles
- Daoyuan Fang, Tailong Li, Global Weak Solutions to the Landau-Lifshitz System in 3D , CUBO, A Mathematical Journal: Vol. 8 No. 2 (2006): CUBO, A Mathematical Journal
- Paul W. Eloe, Positive Operators and Maximum Principles for Ordinary Differential Equations , CUBO, A Mathematical Journal: Vol. 7 No. 2 (2005): CUBO, A Mathematical Journal
- Seyed Mostafa Sajjadi, Ghasem Alizadeh Afrouzi, On a class of fractional \(p(x,y)-\)Kirchhoff type problems with indefinite weight , CUBO, A Mathematical Journal: Vol. 26 No. 1 (2024)
- Shruti A. Kalloli, José Vanterler da C. Sousa, Kishor D. Kucche, On the \(\Phi\)-Hilfer iterative fractional differential equations , CUBO, A Mathematical Journal: Vol. 27 No. 1 (2025)
- Vladik Kreinovich, Engineering design under imprecise probabilities: computational complexity , CUBO, A Mathematical Journal: Vol. 13 No. 1 (2011): CUBO, A Mathematical Journal
- Sirkka-Liisa Eriksson, Heikki Orelma, A simple construction of a fundamental solution for the extended Weinstein equation , CUBO, A Mathematical Journal: Vol. 26 No. 2 (2024)
- Xavier Antoine, Christophe Besse, Jérémie Szeftel, Towards accurate artificial boundary conditions for nonlinear PDEs through examples , CUBO, A Mathematical Journal: Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal
- Ganga Ram Gautam, Sandra Pinelas, Manoj Kumar, Namrata Arya, Jaimala Bishnoi, On the solution of \(\mathcal{T}-\)controllable abstract fractional differential equations with impulsive effects , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- Joss Sánchez P., Characterization of the Banzhaf value using a consistency axiom , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal
- E. A. Grove, E. Lapierre, W. Tikjha, On the global behavior of ð‘¥áµ¤â‚Šâ‚ = |ð‘¥áµ¤|− ð‘¦áµ¤ − 1 and ð‘¦áµ¤â‚Šâ‚ = ð‘¥áµ¤ +|ð‘¦áµ¤| , CUBO, A Mathematical Journal: Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal
<< < 1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 L. Wang et. al.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.