New upper estimate for positive solutions to a second order boundary value problem with a parameter

Downloads

DOI:

https://doi.org/10.56754/0719-0646.2501.121

Abstract

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

Boundary value problem with a parameter , positive solution , upper and lower estimate

Mathematics Subject Classification:

34B18 , 34B27
  • Pages: 121–137
  • Date Published: 2023-04-24
  • Vol. 25 No. 1 (2023)

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.

Downloads

Download data is not yet available.

Published

2023-04-24

How to Cite

[1]
L. Wang and B. Yang, “New upper estimate for positive solutions to a second order boundary value problem with a parameter”, CUBO, pp. 121–137, Apr. 2023.

Issue

Section

Articles