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
- George A. Anastassiou, Foundations of generalized Prabhakar-Hilfer fractional calculus with applications , CUBO, A Mathematical Journal: Vol. 23 No. 3 (2021)
- Cong He, Jingchun Chen, Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\) , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Manuel Saavedra, Helmuth Villavicencio, On the minimum ergodic average and minimal systems , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
- Bapurao C. Dhage, John R. Graef, Shyam B. Dhage, Existence, stability and global attractivity results for nonlinear Riemann-Liouville fractional differential equations , CUBO, A Mathematical Journal: Vol. 25 No. 1 (2023)
- Youssef N. Raffoul, Boundedness and stability in nonlinear systems of differential equations using a modified variation of parameters formula , CUBO, A Mathematical Journal: Vol. 25 No. 1 (2023)
- Raúl Fierro, Sergio Pizarro, Fixed points of set-valued mappings satisfying a Banach orbital condition , CUBO, A Mathematical Journal: Vol. 25 No. 1 (2023)
- Raymond Mortini, A nice asymptotic reproducing kernel , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- Abhijit Banerjee, Arpita Kundu, On uniqueness of \(L\)-functions in terms of zeros of strong uniqueness polynomial , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- Hamza El-Houari, Lalla Saádia Chadli, Hicham Moussa, On a class of fractional Γ(.)-Kirchhoff-Schrödinger system type , CUBO, A Mathematical Journal: Vol. 26 No. 1 (2024)
- Sapan Kumar Nayak, P. K. Parida, Global convergence analysis of Caputo fractional Whittaker method with real world applications , CUBO, A Mathematical Journal: Vol. 26 No. 1 (2024)
<< < 19 20 21 22 23 24 25 26 > >>
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.