Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 5
88
Views
1
CrossRef citations to date
0
Altmetric
Articles

The dual variational method for n-th order ODEs with multipoint boundary conditions

, , &
Pages 957-971 | Received 11 Feb 2013, Accepted 29 Apr 2013, Published online: 07 Jun 2013

References

  • Bonanno G, Bella B. A boundary value problem for fourth-order elastic beam equation. Journal of Mathematical Analysis and Application. 2008;342:1166–1176.
  • Yang X, Lo K. Existence of a positive solution to a fourth-order boundary value problem. Nonlinear Analysis. 2008;69:2267–2273.
  • Yao Q. Positive solutions of a nonlinear elastic beam equation rigidly fastened on the left and simply supported on the right. Nonlinear Analysis. 2008;69:2267–2273.
  • Amster P, Cárdenas Alzate PP. Existence of solutions for some nonlinear beam equations. Portugaliae Mathematica (Nova Série). 2006;63(1):113–125.
  • Bai Z, Wang H. On positive solutions of some nonlinear fourth-order beam equations. Journal of Mathematical Analysis and Application. 2002;270(2):357–368.
  • Liu X-L, Li W-T. Positive solutions of the nonlinear fourth-order beam equation with three parameters. Journal of Mathematical Analysis and Application. 2005;303(1):150–163.
  • Ma TF. Positive solutions for a beam equation on a nonlinear elastic foundation. Mathematical and Computer Modelling. 2004;39(11–12):1195–1201.
  • Sanchez L. Boundary value problems for some fourth order ordinary differential equations. Applied Analysis. 1990;38(3):161–177.
  • Yao Q. Solvability of an elastic beam equation with Caratheodory function. Mathematics with Applications (Wuhan). 2004;17(3):389–392.
  • Galewski M, Smejda J. On the dependence on parameters for mountain pass solutions of second order discrete BVP’s. Applied Mathematical Computation. 2013;219(11):5963–5971.
  • Nowakowski A, Orpel A. Positive solutions for a nonlocal boundary-value problem with vector-valued response. Bulletin of the Belgian Mathematical Society – Simon Stevin. 2003;10(3):409–420.
  • O’Regan D, Orpel A. Eigenvalue problems for singular ODEs. Glasgow Mathematical Journal. 2011;53:301–312.
  • Cao D, Ma R. Positive solutions to a second order multi-point boundary value problem. Electronic Journal of Differential Equations. 2000;2000:1–8.
  • Graef JR, Yang B. Positive solutions to a multi-point higher order boundary value problem. Journal of Mathematical Analysis and Application. 2006;316:409–421.
  • O’Regan D, Orpel A. Eigenvalue intervals for higher order problems with singular nonlinearites. Applied Mathematics and Computation. 2011;218:1233–1239.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.