Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions

ANZIAM Journal

Volumn 44, Issue 3, 2003, Pages 393-407

  Franco, Daniel ^a   Pouso, Rodrigo L ^b  

^a UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747193488     PISSN: 14461811     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1446181100008105     Document Type: Article

References (17)

1. J. Appell and P. P. Zabrejko, Nonlinear superposition operators (Cambridge University Press 1990).
2. A. Cabada and E. Liz, "Discontinuous impulsive differential equations with nonlinear boundary conditions". Nonlinear Anal. 28 (1997) 1491-1497.
3. A. Cabada and E. Liz, "Boundary value problems for higher order ODEs with impulses", Nonlinear Anal. 32 (1998) 775-786.
4. A. Cabada and R. L. Pouso, "On first-order discontinuous scalar differential equations", Nonlinear Studies 6 (1999) 161-170.
5. L. H. Erbe, H. I. Freedman, X. Z. Liu and J. H. Wu, "Comparison principles for impulsive parabolic equations with applications to models of single-species growth", J. Austral. Math. Soc. Ser. B 32 (1991) 382-400.
6. D. Franco and J. J. Nieto, "A new maximum principle for impulsive first-order problems". Internat. J. Theoret. Phys. 37 (1998) 1607-1616.
7. M. Frigon and D. O'Regan, "Existence results for first-order impulsive differential equations", J. Math. Anal. Appl. 193 (1995) 96-113.
8. E. R. Hassan and W. Rzymowski, "Extremal solutions of a discontinuous differential equation", Nonlinear Anal. 37 (1999) 997-1017.
9. S. Heikkilä, "First-order discontinuous differential equations with functional boundary conditions", in Advances in nonlinear dynamics. Stability Control Theory Methods Appl. 5, (Gordon and Breach, Amsterdam, 1997) 273-281.
10. S. Heikkilä and V. Lakshmikantham, Monotone iterative techniques for discontinuous nonlinear differential equations (Marcel Dekker, New York, 1994).
11. E. Kruger-Thiemer, "Formal theory of drug dosage regiments, I", J. Theoret. Biol. 13 (1966) 212-235.
12. E. Kruger-Thiemer, "Formal theory of drug dosage regiments, II", J. Theoret. Biol. 23 (1969) 169-190.
13. V. Lakshmikantham, D. D. Bainovand P. S. Simeonov, Theory of impulsive differential equations (World Scientific, Singapore, 1989).
14. X. Liu and A. Willms, "Impulsive stabilizability of autonomous systems", J. Math. Anal. Appl. 187(1994) 17-39.
15. E. Liz and J. J. Nieto, "Positive solutions of linear impulsive differential equations". Commun. Appl. Anal. 2 (1998) 565-571.
16. J. J. Nieto, "Basic theory for nonresonance impulsive periodic problems of first order", J. Math. Anal. Appl. 205 (1997) 423-433.
17. Y. V. Rogovchenko, "Nonlinear impulse evolution systems and applications to population models", J. Math. Anal. Appl. 207 (1997) 300-315.