Three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 2, 2008, Pages 569-578

  He, Zhimin ^a   Long, Zhiwen ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Boundary value problem; Five functionals fixed point theorem; p Laplacian; Positive solution; Time scale

Indexed keywords

DYNAMIC PROGRAMMING; FUNCTIONAL ANALYSIS; LAPLACE EQUATION; PROBLEM SOLVING; THEOREM PROVING;

FIVE-FUNCTIONALS FIXED-POINT THEOREM; POSITIVE SOLUTION; TIME SCALES;

BOUNDARY VALUE PROBLEMS;

EID: 44149093820     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.06.001     Document Type: Article

References (28)

1. Agarwal R.P., and Bohner M. Basic calculus on time scales and some of its applications. Results. Math. 35 (1999) 3-22
2. Agarwal R.P., Lü H., and O'Regan D. Eigenvalues and the one-dimensional p-Laplacian. J. Math. Anal. Appl. 266 (2002) 383-400
3. Anderson D., Avery R.I., and Henderson J. Existence of solutions for a one dimensional p-Laplacian on time-scales. J. Difference Equ. Appl. 10 (2004) 889-896
4. Atici F.M., and Guseinov G.S. On Green's functions and positive solutions for boundary value problems on time scales. J. Comput. Anal. Math. 141 (2002) 75-99
5. Avery R.I. A generalization of the Leggett-Williams fixed point theorem. Math. Sci. Res. Hot-Line. 2 (1998) 9-14
6. Avery R.I., and Anderson D. Existence of three positive solutions to a second-order boundary value problem on a measure chain. J. Comput. Appl. Math. 141 (2002) 65-73
7. Avery R.I., and Henderson J. Three symmetric positive solutions for a second-order boundary value problem. Appl. Math. Lett. 13 3 (2000) 1-7
8. Avery R.I., and Henderson J. Existence of three positive pseudo-symmetric solutions for a one-dimensional p-Laplacian. J. Math. Anal. Appl. 277 (2003) 395-404
9. Avery R.I., and Henderson J. Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian. J. Difference Equ. Appl. 10 (2004) 529-539
10. Bai C.Z., and Fan J.X. Existence of multiple positive solutions for nonlinear m-point boundary value problems. J. Math. Anal. Appl. 281 (2003) 76-83
11. Bohner M., and Peterson A. Dynamic Equations on Time Scales: An Introduction with Applications (2001), Birkhäuser, Boston
12. Bohner M., and Peterson A. Advances in Dynamic Equations on Time Scales (2002), Birkhäuser, Boston
13. Cabada A. Extremal solutions for the difference φ{symbol}-Laplacian problem with nonlinear functional boundary conditions. Comput. Math. Appl. 42 (2001) 593-601
14. Chyan C.J., and Henderson J. Eigenvalue problems for nonlinear differential equations on a measure chain. J. Math. Anal. Appl. 245 (2000) 547-559
15. Deimling K. Nonlinear Functional Analysis (1985), Springer-Verlag, New York
16. Guo Y.P., and Ge W.G. Three positive solutions for the one-dimensional p-Laplacian. J. Math. Anal. Appl. 286 (2003) 491-508
17. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, Inc.
18. He Z.M. On the existence of positive solutions of p-Laplacian difference equations. J. Comput. Appl. Math. 161 (2003) 193-201
19. He Z.M. Double positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. J. Comput. Appl. Math. 182 (2005) 304-315
20. Hilger S. Analysis on measure chains-a unified approach to continuous and discrete calculus. Results. Math. 18 (1990) 18-56
21. Lakshmikantham V., Sivasundaram S., and Kaymakcalan B. Dynamical Systems on Measure Chains (1996), Kluwer Academic, Boston
22. Leggett R.W., and Williams L.R. Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana Univ. Math. J. 28 (1979) 673-688
23. Liu Y., and Ge W. Multiple positive solutions to three-point boundary value problem with p-Laplacian operator. J. Math. Anal. Appl. 277 (2003) 293-302
24. Liu Y., and Ge W. Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator. J. Math. Anal. Appl. 278 (2003) 551-561
25. Song C., and Xiao C. Positive solutions for p-Laplacian functional dynamic equations on time scales. Nonlinear Anal. TMA 66 (2007) 1989-1998
26. Wang J.Y. The existence of positive solutions for the one-dimensional p-Laplacian. Proc. Amer. Math. Soc. 125 (1997) 2275-2283
27. Wang J.Y., and Zheng D.W. On the existence of positive solutions to a three-point boundary value problem for the one-dimensional p-Laplacian. Z. Angew. Math. Mech. 77 (1997) 477-479
28. Wang H.Y. On the number of positive solutions of nonlinear systems. J. Math. Anal. Appl. 281 (2003) 287-306