Existence of solutions for a first-order p-Laplacian BVP on time scales

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 12, 2008, Pages 4521-4525

  Anderson, Douglas R ^a  

^a and Exercise Science   (United States)

Author keywords

Cone; Delta dynamic equation; Fixed point theorems; One dimensional p Laplacian

Indexed keywords

SOLUTIONS;

DELTA DYNAMIC EQUATION; DYNAMIC EQUATIONS; EXISTENCE OF SOLUTIONS; FIRST-ORDER; FIXED POINT THEOREMS; LAPLACIAN; ON TIMES; ONE-DIMENSIONAL P-LAPLACIAN; POSITIVE SOLUTIONS;

LAPLACE TRANSFORMS;

EID: 55049128075     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.11.008     Document Type: Article

References (28)

1. Allegretto W., and Huang X.Y. A Picone's identity for the p-Laplacian and applications. Nonlinear Anal. 32 (1998) 819-830
2. Aronson D.G., and Caffarelli L.A. The initial trace of a solution of the porous medium equation. Trans. Amer. Math. Soc. 280 (1983) 351-366
3. Bertsch M., and Hilhorst D. The interface between regions where u < 0 and u > 0 in the porous medium equation. Appl. Anal. 41 (1991) 111-130
4. Galaktionov V.A., and Vazquez J.L. Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations. Math. Ann. 303 (1995) 741-769
5. Henderson J., and Thompson H.B. Multiple symmetric positive solutions for a second order boundary value problem. Proc. Amer. Math. Soc. 128 (2000) 2373-2379
6. Sakaguchi S. Regularity of the interfaces with sign changes of solutions of the one-dimensional porous medium equation. J. Differential Equations 178 (2002) 1-59
7. Wang J. The existence of positive solutions for the one-dimensional p-Laplacian. Proc. Amer. Math. Soc. 125 (1997) 2275-2283
8. Anderson D.R., Avery R.I., and Henderson J. Existence of solutions for a one-dimensional p-Laplacian on time scales. J. Difference Equ. Appl. 10 10 (2004) 889-896
9. Cabada A. Existence results for p-Laplacian boundary value problems on time scales. Adv. Differential Equations (2006) 11 Article ID 21819
10. Cabada A. Discontinuous functional p-Laplacian boundary value problems on time scales. Int. J. Differ. Equ. 2 1 (2007) 51-60
11. He Z. Double positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales. Appl. Anal. 84 (2005) 377-390
12. He Z. Double positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. J. Comput. Appl. Math. 182 2 (2005) 304-315
13. He Z., and Jiang X. Triple positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales. J. Math. Anal. Appl. 321 2 (2006) 911-920
14. He Z., and Long Z. Three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. Nonlinear Anal. (2007) 10.1016/j.na.2007.06.001
15. Hong S. Triple positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. J. Comput. Appl. Math. 206 2 (2007) 967-976
16. Sang Y., and Xi H. Positive solutions of nonlinear m-point boundary-value problem for p-Laplacian dynamic equations on time scales. Electron. J. Differential Equations 2007 34 (2007) 1-10
17. Song C., and Xiao C. Positive solutions for p-Laplacian functional dynamic equations on time scales. Nonlinear Anal. 66 9 (2007) 1989-1998
18. Song C., and Weng P. Multiple positive solutions for p-Laplacian functional dynamic equations on time scales. Nonlinear Anal. 68 (2008) 208-215
19. Su Y.H., Li W.-T., and Sun H.-R. Triple positive pseudo-symmetric solutions of three-point BVPs for p-Laplacian dynamic equations on time scales. Nonlinear Anal. (2007) 10.1016/j.na.2006.12.042
20. Sun H.-R., Tang L.-T., and Wang Y.-H. Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales. J. Math. Anal. Appl. 331 1 (2007) 248-262
21. Sun H.-R., and Li W.-T. Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales. J. Differential Equations 240 (2007) 217-248
22. Wang D.-B. Existence, multiplicity and infinite solvability of positive solutions for p-Laplacian dynamic equations on time scales. Electron. J. Differential Equations 2006 96 (2006) 1-10
23. Wang D.-B. Three positive solutions for p-Laplacian functional dynamic equations on time scales. Electron. J. Differential Equations 2007 95 (2007) 1-9
24. Wang D.-B. Three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. Nonlinear Anal. (2007) 10.1016/j.na.2007.01.037
25. Hilger S. Analysis on measure chains - a unified approach to continuous and discrete calculus. Results Math. 18 (1990) 18-56
26. Bohner M., and Peterson A. Dynamic Equations on Time Scales, An Introduction with Applications (2001), Birkhäuser, Boston
27. In: Bohner M., and Peterson A. (Eds). Advances in Dynamic Equations on Time Scales (2003), Birkhäuser, Boston
28. Krasnosel'skii M.A. Positive Solutions of Operator Equations (1964), Noordhoff, Groningen