- Aftabizadeh , A.R. , Huang , Y.K. and Pavel , N.H. 1995 . Nonlinear Third-Order Differential Equations with Anti-Periodic Boundary Conditions and Some Optimal Control Problems . J. Math. Anal. Appl. , 192 : 266 – 293 .
- Aftabizadeh , A.R. , Xu , J. and Gupta , C.P. 1990 . Periodic Boundary Value Problems for Third-Order Ordinary differential Equations . Nonlinear Anal. , 14 : 1 – 10 .
- Afuwape , A.U. , Omari , P. and Zanolin , F. 1989 . Nonlinear Perturbations of Differential Operators with Nontrivial Kernel and Applications to Third-Order Periodic Boundary Value Problems . J. Math. Anal. Appl. , 143 : 35 – 56 .
- Cabada , A. 1994 . The Method of Lower and Upper solutions for Second, Third, Fourth and Higher Order Boundary Value Problems . J. Math. Anal. Appl. , 185 : 302 – 320 .
- Cabadai A. The method of Lower and Upper solutions for Third-Order Periodic Boundary Value Problems J. Math. Anal. Appl. (to appear).
- Erbe , L.H. and Guo , D. 1992 . Periodic Boundary Value Problems for Second Order Integrodifferential Equations of Mixed Type . Appl. Anal. , 46 : 249 – 258 .
- Gregus , M. 1987 . Third Order Linear Differential Equations , Dordrecht : Reidel .
- Hu , S. and Lakshmikantham , V. 1986 . Periodic Boundary Value Problem for Second Order Integro-Differential Equations of Volterra Type . Appl. Anal. , 21 : 199 – 205 .
- Liz , E. and Nieto , J.J. 1994 . Periodic Boundary Value Problem for Integro-Differential Equations with General Kernel . Dynam. Syst. Appl. , 3 : 297 – 304 .
- Nieto , J.J. 1992 . “ Periodic Solutions for Third Order Nonlinear Ordinary Differential Equations ” . In Recent Trends in Differential Equations , 463 – 470 . Singapore : World Scientific .
- Nieto , J.J. 1995 . Periodic Boundary Value Problems for Second Order Integro-Ordinary Differential Equation with General Kernel and Carathéodory Nonlinearities . Int. J. Math. Math. Sci. , 18 : 757 – 764 .
Order reduction for periodic boundary value problems of discontinuous third-order differential equations
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.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.