Double positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales

International Journal of Phytoremediation

Volumn 84, Issue 4, 2005, Pages 377-390

  He, Zhimin ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

AMS Subject Classification: 39A10; Boundary value problem; P Laplacian; Positive solution; Time scale; Twin fixed point theorem

Indexed keywords

EID: 84963960219     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810500047956     Document Type: Article

References (27)

1. Lakshmikantham V, Sivasundaram S, Kaymakcalan B, 1996 Dynamical Systems on Measure Chains Boston Kluwer Academic
2. Bohner M, Peterson A, 2001 Dynamic Equations on Time Scales: An Introduction with Applications Boston Birkhäuser
3. Bohner M, Peterson A, 2002 Advances in Dynamic Equations on Time Scales Boston Birkhäuser
4. Hilger, S. 1990. Analysis on measure chains–a unified approach to continuous and discrete calculus. Results in Mathematics, 18: 18–56.
5. Agarwal, RP, and Bohner, M. 1999. Basic calculus on time scales and some of its applications. Results in Mathematics, 35: 3–22.
6. Atici, FM, and Guseinov, GSh., 2002. On Green's functions and positive solutions for boundary value problems on time scales. Journal of Computational and Applied Mathematics, 141: 75–99.
7. Chyan, CJ, and Henderson, J. 2000. Eigenvalue problems for nonlinear differential equations on a measure chain. Journal of Mathematical Analysis and Applications, 245: 547–559.
8. Agarwal, RP, and O'Regan, D. 2001. Nonlinear boundary value problems on time scales. Nonlinear Analysis, 44: 527–535.
9. Wang, JY. 1997. The existence of positive solutions for the one-dimensional p-Laplacian. Proceedings of American Mathematical Society, 125: 2275–2283.
10. Wang, JY, and Zheng, DW. 1997. On the existence of positive solutions to a three-point boundary value problem for the one-dimensional p-Laplacian. Journal of Applied Mathematics and Mechanics, 77: 477–479.
11. Cabada, A. 2001. Extremal solutions for the difference ϕ-laplacian problem with nonlinear functional boundary conditions. Computers & Mathematics with Applications, 42: 593–601.
12. Agarwal, RP, Lü, H, and O'Regan, D. 2002. Eigenvalues and the one-dimensional p-Laplacian. Journal of Mathematical Analysis and Applications, 266: 383–400.
13. Bai, CZ, and Fan, JX. 2003. Existence of multiple positive solutions for nonlinear m-point boundary value problems. Journal of Mathematical Analysis and Applications, 281: 76–83.
14. Avery, RI, and Henderson, J. 2003. Existence of three positive pseudo-symmetric solutions for a one-dimensional p-Laplacian. Journal of Mathematical Analysis and Applications, 277: 395–404.
15. Avery, RI, and Henderson, J. 2004. Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian. Journal of Difference Equations and Applications, 10: 529–539.
16. Wang, HY. 2003. On the number of positive solutions of nonlinear systems. Journal of Mathematical Analysis and Applications, 281: 287–306.
17. He, ZM. 2003. On the existence of positive solutions of p-Laplacian difference equations. Journal of Computational and Applied Mathematics, 161: 193–201.
18. Guo, YP, and Ge, WG. 2003. Three positive solutions for the one-dimensional p-Laplacian. Journal of Mathematical Analysis and Applications, 286: 491–508.
19. Anderson, D, Avery, RI, and Henderson, J. 2004. Existence of solutions for a one dimensional p-Laplacian on time scales. Journal of Difference Equations and Applications, 10: 889–896.
20. Avery, RI, and Henderson, J. 2001. Twin positive fixed points of nonlinear operators on ordered Banach spaces. Communications on Applied Nonlinear Analysis, 8: 27–36.
21. Avery, RI, Chyan, CJ, and Henderson, J. 2001. Twin solutions of a boundary value problems for ordinary differential equations and finite difference equations. Computers & Mathematics with Applications, 42: 695–704.
22. Chyan, CJ, and Henderson, J. 2002. Twin solutions of boundary value problems for differential equations on measure chains. Journal of Computational and Applied Mathematics, 141: 123–131.
23. Henderson, J. 2002. Double solutions of impulsive dynamic boundary value problems on a time scale. Journal of Difference Equations and Applications, 8: 345–356.
24. Liu, Y, and Ge, W. 2003. Multiple positive solutions to three-point boundary value problem with p-Laplacian operator. Journal of Mathematical Analysis and Applications, 277: 293–302.
25. Liu, Y, and Ge, W. 2003. Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator. Journal of Mathematical Analysis and Applications, 278: 551–561.
26. Anderson, D. 2002. Solutions to second-order three-point problems on time scales. Journal of Difference Equations and Applications, 8: 673–688.
27. Kaufmann, ER. 2003. Positive solutions of a three-point boundary-value problem on a time scale. Electronic Journal of Differential Equations, 82: 1–11.