Existence result for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control

Journal of Mathematical Analysis and Applications

Volumn 309, Issue 1, 2005, Pages 271-283

  Grossinho, M R ^a   Minhos F M ^b   Santos, A I ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b UNIVERSITY OF ÉVORA   (Portugal)

Author keywords

A priori estimates; Leray Schauder degree; Lower and upper solutions; Sign type Nagumo condition; Third order nonlinear boundary value problems

Indexed keywords

EID: 22144438705     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.01.030     Document Type: Article

References (17)

1. A. Cabada M.R. Grossinho F. Minhós On the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions J. Math. Anal. Appl. 285 2003 174-190
2. A. Cabada R.L. Pouso Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions Nonlinear Anal. 42 2000 1377-1396
3. A. Cabada R.L. Pouso Existence results for the problem (φ(u′))′ = f(t,u,u′) with nonlinear boundary conditions Nonlinear Anal. 35 1999 221-231
4. C. de Coster, La méthode des sur et sous solutions dans l'étude de problèmes aux limites, Université Catholique de Louvain, Faculté des Sciences, Départment de Mathématique, Février 1994
5. C. de Coster, P. Habets, Upper and lower solutions in the theory of ODE boundary value problems: Classical and recent results, Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Recherches de Mathématique, 52, April 1996
6. Z. Du W. Ge X. Lin Existence of solutions for a class of third-order nonlinear boundary value problems J. Math. Anal. Appl. 294 2004 104-112
7. M. Grossinho F. Minhós Existence result for some third order separated boundary value problems Nonlinear Anal. 47 2001 2407-2418
8. M. Grossinho, F. Minhós, Upper and lower solutions for higher order boundary value problems, preprint CMAF, Mat-UL-2001-19
9. M. Grossinho, F. Minhós, Solvability of some higher order two-point boundary value problems, Equadiff 10, CD-ROM papers, 2001, pp. 183-189
10. M. Grossinho, F. Minhós, A.I. Santos, A third order boundary value problem with one-sided Nagumo condition, Nonlinear Anal., in press
11. M. Grossinho, F. Minhós, A.I. Santos, Solvability of some third order boundary value problem with asymmetric unbounded nonlinearities, in preparation
12. P. Habets R.L. Pouso Examples of the nonexistence of a solution in the presence of upper and lower solutions ANZIAM J. 44 2003 591-594
13. J. Mawhin Topological Degree Methods in Nonlinear Boundary Value Problems Regional Conf. Ser. in Math. vol. 40 1979 Amer. Math. Soc. Providence, RI
14. F. Minhós, T. Gyulov, A.I. Santos, Existence and location result for a fourth order boundary value problems, Proc. Fifth Internat. Conf. on Dynamical Systems and Differential Equations, USA, 2004, in press
15. F. Minhós, A.I. Santos, Existence and non-existence results for two-point boundary value problems of higher order, Proc. Equadiff 2003, in press
16. M. Nagumo Über die differentialgleichung y″ = f(t,y,y′) Proc. Phys.-Math. Soc. Japan 19 1937 861-866
17. M. Nagumo On principally linear elliptic differential equations of the second order Osaka Math. J. 6 1954 207-229