Multiple periodic solutions for a second-order problem on periodic time scales

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 1, 2005, Pages 101-115

  Anderson, Douglas R ^a  

^a and Exercise Science   (United States)

Author keywords

Boundary value problems; Fixed points; Riccati equation; Time scales

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; RICCATI EQUATIONS; SET THEORY; THEOREM PROVING;

EXPONENTIAL FUNCTIONS; FIXED POINTS; SUBSETS; TIME SCALES;

NONLINEAR EQUATIONS;

EID: 9344255521     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.08.024     Document Type: Article

References (15)

1. R.P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, Results Math. 35(1999) 3-22.
2. D.R. Anderson, Positivity of Green's function for an n-point right focal boundary value problem on measure chains, Math. Comput. Model. 31 (2000) 29-50.
3. F.M. Atici, G.Sh. Guseinov, Positive periodic solutions for nonlinear difference equations with periodic coefficients, J. Math. Anal. Appl. 232 (1999) 166-182.
4. M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
5. M. Bohner, A. Peterson (Eds.), Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
6. L. Erbe, A.C. Peterson, Green's functions and comparison theorems for differential equations on measure chains, Dynam. Contin. Discrete Impulse Systems 6 (1) (1999) 121-137.
7. L. Erbe, A.C. Peterson, Positive solutions for a nonlinear differential equation on a measure chain, Math. Comput. Model. 32 (5-6) (2000) 571-585.
8. L. Erbe, A.C. Peterson, Eigenvalue conditions and positive solutions, J. Differential Equations Appl. 6 (2) (2000) 165-191.
9. L. Erbe, R. Mathsen, A.C. Peterson, Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain, J. Comput. Appl. Math. 113 (1-2) (2000) 365-380.
10. Y. Liu, W. Ge, Three positive periodic solutions of nonlinear differential equations with periodic coefficients, Anal. Appl. 2003, preprint.
11. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18 (1990) 18-56.
12. J. Hoffacker, Green's functions for higher order equations on time scales, PanAm. Math. J. 11 (4) (2001) 1-28.
13. B. Kaymakçalan, V. Lakshmikantham, S. Sivasundaram, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.
14. M.A. Krasnoselskii, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964.
15. R.W. Leggett, L.R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J. 28 (1979) 673-688.