Existence theorems for nonlinear problems by continuation methods

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3313-3322

  Precup, Radu ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Coincidence theorems; Continuation methods; Essential map; Fixed point; Impulsive differential equations; Periodic solutions; Singular differential equations

Indexed keywords

EID: 0042045517     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00333-1     Document Type: Article

References (22)

1. BOBISUD L. E. & O'REGAN D., Positive solutions for a class of nonlinear singular boundary value problems at resonance, J. math. Analysis Applic. 184, 263-284 (1994).
2. CAPIETTO A., MAWHIN J. & ZANOLIN F., A continuation approach to superlinear periodic boundary value problems, J. diff. Egns. 88, 347-395 (1990).
3. CAPIETTO A., MAWHIN J. & ZANOLIN F., Continuation theorems for periodic perturbations of autonomous systems, Trans. Am. math. Soc. 329, 41-72 (1992).
4. FITZPATRICK P. M., MASSABÒ I. & PEJSACHOWICZ J., Complementing maps, continuation and global bifurcation, Bull. Am. math. Soc. 9, 79-81 (1983).
5. FRIGON M. & GRANAS A., Résultats du type de Leray-Schauder pour des contractions multivoques, Topol. Methods Nonlinear Anal. 4, 197-208 (1994).
6. FURI M. & PERA M. P., On the existence of an unbounded connected set of solutions for nonlinear equations in Banach spaces, Atti Accad. Naz. Lincei Rend. Sc. Fis. Mat. Natur. 67, 31-38 (1979).
7. GAINES R. E. & MAWHIN J., Coincidence degree and nonlinear differential equations, in Lecture Notes in Mathematics, Vol. 568. Springer, Berlin (1977).
8. GEBA K., GRANAS A., KACZYNSKI T. & KRAWCEWICZ W., Homotopie et équations non linéaires dans les espaces de Banach, C. R. Acad. Sci. Paris 300, 303-306 (1985).
9. GRANAS A., Continuation method for contractive maps, Topol. Methods Nonlinear Anal. 3, 375-379 (1994).
10. GRANAS A., GUENTHER R. B. & LEE J. W., Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math, pures appl. 70, 153-196 (1991).
11. KIRR E. & PRECUP R., Periodic solutions of superlinear impulsive differential systems, preprint, Department of Mathematics, Babes-Bolyai University of Cluj (1995).
12. KRAWCEWICZ W., Contribution à la théorie des équations non linéaires dans les espaces de Banach, in Dissertationes Mathematic ae, Vol. 263. PWN, Warsaw (1988).
13. LAKSHMIKANTHAM V., BAINOV D. D. & SIMEONOV P. S., Theory of Impulsive Differential Equations. World Scientific, Singapore (1989).
14. MAWHIN J., Continuation theorems and periodic solutions of ordinary differential equations, in Topological Methods in Differential Equations and Inclusions (Edited by A. GRANAS and M. FRIGON), pp. 291-376. Kluwer, Dordrecht (1995).
15. O'REGAN D., Theory of Singular Boundary Value Problems. World Scientific, Singapore (1994).
16. O'REGAN D., Differential equations at resonance, Commentat. math. Univ. Carol. 36, 673-694 (1995).
17. PRECUP R., On the topological transversality principle, Nonlinear Analysis 20, 1-9 (1993).
18. PRECUP R., On some fixed point theorems of Deimling, Nonlinear Analysis 23, 1315-1320 (1994).
19. PRECUP R., Foundations of the continuation principles of Leray-Schauder type, Proceedings of the 23rd Conference on Geometry and Topology, September 1993, Cluj, Romania, pp. 136-140. Univ. Babes-Bolyai, Cluj (1994).
20. PRECUP R., A Granas type approach to some continuation theorems and periodic boundary value problems with impulses, Topol. Methods Nonlinear Anal. 5, 385-396 (1995).
21. PRECUP R., Continuation principles for coincidences, Mathematica (Cluj) (to appear).
22. PRECUP R., Periodic solutions of superlinear singular ordinary differential equations (to appear).