Nagumo type existence results for second-order nonlinear dynamic BVPS

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 2, 2005, Pages 209-220

  Atici, F M ^a   Cabada, A ^b   Chyan, C J ^c   Kaymakcalan B ^d  

^a WESTERN KENTUCKY UNIVERSITY   (United States)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^c TAMKANG UNIVERSITY   (Taiwan)

^d GEORGIA SOUTHERN UNIVERSITY   (United States)

Author keywords

Lower and upper solutions; Nagumo condition; Time scales

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DYNAMICS; FUNCTIONS; LINEAR EQUATIONS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

GROWTH CONDITIONS; LOWER AND UPPER SOLUTIONS; NAGUMO CONDITION; TIME SCALES;

DIFFERENTIAL EQUATIONS;

EID: 10044298312     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.07.036     Document Type: Article

References (16)

1. A. Adje. Sur et Sous-Solutions dans les Equations Differentielles Discontinues avec des Conditions aux Limites non Linéaires, Ph. D., Université Catholique de Louvain-la-Neuve, 1987.
2. M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
3. A. Cabada, V. Otero-Espinar, R.L. Pouso, Existence and approximation of solutions for discontinuous first order difference problems with nonlinear functional boundary conditions in the presence of lower and upper solutions, Comput. Math. Appl. 39 (2000) 21-33.
4. A. Cabada, D.R. Vivero, Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral, Application to the calculus of Δ-antiderivatives, preprint.
5. P.W. Eloe, A boundary value problem for a system of difference equations, Nonlinear Anal. 7 (1983) 813-820.
6. D. Franco, D. O'Regan, Existence of solutions to second order problems with nonlinear boundary conditions, Dynamical Systems and Differential Equations (Wilmington, NC, 2002); Discrete Contininuous Dyn. Syst. Suppl. (2003) 273-280.
7. D. Franco, D. O'Regan, Existence of solutions to second order problems with nonlinear boundary conditions, Dynamical Systems and Differential Equations (Wilmington, NC, 2002); Discrete Contininuous Dyn. Syst. Suppl. (2003) 273-280.
8. P. Habets, R.L. Pouso, Examples on the nonexistence of a solution in the presence of upper and lower solutions, Anziam J. 44 (2003) 591-594.
9. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18 (1990) 18-56.
10. B. Kaymakçalan, V. Laksmikantham, S. Sivasundaram, Dynamical Systems on Measure Chains, Kluwer, Boston, 1996.
11. G.S. Ladde, V. Lakshmikantham, A.S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston MA, 1985.
12. M. Nagumo, Ueber die Differentialgleichung y" = f(x, y, y'), Proc. Phys.-Math. Soc. Japan 19 (3) (1935) 861-866.
13. M. Nagumo, On principally linear elliptic differential equations of the second order, Osaka Math. J. 6 (1954) 207-229.
14. E. Picard, Sur lapplication des methodes d'approximations successives a l'étude de certaines équations différentielles ordinaires, J. de Math. 9 (1893) 217-271.
15. O. Scorza Dragoni, II probleme dei valori ai limiti studiato in grande per gli integrali di una equazione differenzile del secondo ordine, Giornale Mat. (Battaglini) 69 (1931) 77-112.
16. W. Zhuang, Y. Chen, S.S. Cheng, Monotone methods for a discrete boundary problem, Comput. Math. Appl. 32 (1996) 41-49.