Discontinuous first-order functional boundary value problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 7, 2008, Pages 2142-2149

  Sestelo, Rubén Figueroa ^a   Pouso, Rodrigo López ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Boundary value problems; Discontinuous differential equations; Functional differential equations

Indexed keywords

BESSEL FUNCTIONS; BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); FISH; INITIAL VALUE PROBLEMS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; SET THEORY; THEOREM PROVING;

(I ,J) CONDITIONS; (SPM) CLASSES; BOUNDARY VALUES; ELSEVIER (CO); EXISTENCE RESULTS; FIRST ORDERS; FUNCTIONAL DIFFERENTIAL EQUATIONS; GENERAL (CO); MONOTONICITY; TIME-DEPENDENT;

BOUNDARY CONDITIONS;

EID: 45449084283     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.07.051     Document Type: Article

References (17)

1. Aubin J.P., and Cellina A. Differential Inclusions (1984), Springer-Verlag, Berlin, Heidelberg
2. Biles D.C. Existence of solutions for discontinuous differential equations. Differential Integral Equations 8 (1995) 1525-1532
3. Carl S., and Heikkilä S. Nonlinear Differential Equations in Ordered Spaces (2000), Chapman & Hall/CRC, Boca Raton, FL
4. Chen L., and Sun J. Nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type. J. Math. Anal. Appl. 325 2 (2007) 830-842
5. Cid J.Á. On extending existence theory from scalar ordinary differential equations to infinite quasimonotone systems of functional equations. Proc. Amer. Math. Soc. 133 9 (2005) 2661-2670
6. Cid J.Á., and Pouso R.L. Ordinary differential equations and systems with time-dependent discontinuity sets. Proc. Roy. Soc. Edinburgh Sect. A 134 4 (2004) 617-637
7. Franco D., and Pouso R.L. Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions. ANZIAM J. 44 (2003) 393-407
8. Guo D., and Liu X. Extremal solutions for a boundary value problem of nth-order impulsive integro-differential equations in a Banach space. Dynam. Contin. Discrete Impuls. Syst. Ser. A Math. Anal 13 5 (2006) 599-619
9. Hassan E.R., and Rzymowski W. Extremal solutions of a discontinuous differential equation. Nonlinear Anal. 37 (1999) 997-1017
10. Heikkilä S. On the solvability of implicit functional equations with applications to discontinuous differential equations. Acta Math. Sin. (Engl. Ser.) 22 1 (2006) 223-232
11. Heikkilä S., and Lakshmikantham V. Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations (1994), Marcel Dekker, New York
12. Heikkilä S., and O'Regan D. On discontinuous functional Volterra integral equations and impulsive differential equations in abstract spaces. Glasg. Math. J. 46 3 (2004) 529-536
13. Nieto J.J., and Rodríguez-López R. Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations. J. Math. Anal. Appl. 318 2 (2006) 593-610
14. Pouso R.L. Upper and lower solutions for first-order discontinuous ordinary differential equations. J. Math. Anal. Appl. 244 (2000) 466-482
15. Pouso R.L. Necessary conditions for solving initial value problems with infima of superfunctions. Math. Inequal. Appl. 8 4 (2005) 633-641
16. Pouso R.L., and Tomeček J. First- and second-order discontinuous functional differential equations with impulses at fixed moments. Nonlinear Anal. 67 (2007) 455-467
17. West I.H., and Vatsala A.S. Generalized monotone iterative method for integro differential equations with periodic boundary conditions. Math. Inequal. Appl. 10 1 (2007) 151-163