Monotone iterative techniques in ordered Banach spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 8, 1997, Pages 5179-5190

  Liz, Eduardo ^a  

^a NONE

Author keywords

Boundary value problem; Lower and upper solutions; Minimal and maximal fixed points; Monotone iterative technique; Partial order

Indexed keywords

EID: 0000312293     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00224-6     Document Type: Article

References (13)

1. APPEL J. & ZABREIKO P.P. Nonlinear Superposition Operators. Cambridge University Press (1990).
2. CABADA A., The Method of Lower and Upper Solutions for Second, Third, Fourth and Higher Order Boundary Value Problems. J. Math. Anal. Appl. 185, 302-320 (1994).
3. DEIMLING K., Nonlinear Functional Analysis. Springer-Verlag, New York (1985).
4. FUCIK S., Solvability of Nonlinear Equations and Boundary Value Problems. D. Reidel, Dordrecht (1980).
5. HEIKKILÄ S., LAKSHMIKANTHAM V. & SUN Y., Fixed Point Results in Ordered Normed Spaces with Applications to Abstract and Differential Equations. J. Math. Anal. Appl. 163, 422-437 (1992).
6. LAKSHMIKANTHAM V., BAINOV D.D. & SIMEONOV P.S., Theory of impulsive differential equations. World Scientific, Singapore (1989).
7. LIZ E., Existence and Approximation of Solutions for Impulsive First Order Problems with Nonlinear Boundary Conditions. Nonlinear Anal. 25, 1191-1198 (1995).
8. LIZ E., Abstract Monotone Iterative Techniques and Applications to Impulsive Differential Equations. Dynamics of Continuous, Discrete and Impulsive Systems, (To appear).
9. LIZ E. & NIETO J.J., An Abstract Monotone Iterative Method and Applications. Preprint.
10. NIETO J.J., An Abstract Monotone Iterative Technique. Nonlinear Anal. (To appear).
11. POPOV E. P., Theory of Nonlinear Systems of Automatic Regulation and Control. 2nd ed., Nauka, Moscow (1988).
12. ŠEDA V., NIETO J.J. & GERA M., Periodic Boundary Value Problems for Nonlinear Higher Order Ordinary Differential Equations. Appl. Math. Comput. 48, 71-82 (1992).
13. XU H.K. & LIZ E., Boundary Value Problems for Differential Equations with Maxima. Nonl. Studies, (To appear).