Existence of positive solutions for non local p-Laplacian thermistor problems on time scales

Journal of Inequalities in Pure and Applied Mathematics

Volumn 8, Issue 3, 2007, Pages

  Ammi, Moulay Rchid Sidi ^a   Torres, Delfim F M ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Existence; p Laplacian; Positive solutions; Time scales

Indexed keywords

EID: 35348814442     PISSN: None     EISSN: 14435756     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. R.P. AGARWAL AND M. BOHNER, Basic calculus on time scales and some of its applications, Result. Math., 35 (1999), 3-22.
2. R.P. AGARWAL, M. BOHNER, D. O'REGAN AND A. PETERSON, Dynamic equations on time scales: a survey, J. Comput. Appl. Math., 142 (2002), 1-26.
3. R.P. AGARWAL, M. BOHNER AND P. WONG, Sturm-Liouville eigenvalue problem on time scales, Appl. Math. Comput., 99 (1999), 153-166.
4. R.P. AGARWAL AND D. O'REGAN, Nonlinear boundary value problems on time scales, Nonlinear Anal., 44 (2001), 527-535.
5. F.M. ATICI AND G.Sh. GUSEINOV, On Green's functions and positive solutions for boundary-value problems on time scales, J. Comput. Appl. Math., 141 (2002), 75-99.
6. J.W. BEBERNES AND A.A. LACEY, Global existence and finite-time blow-up for a class of non-local parabolic problems, Adv. Diff. Eqns., 2 (1997), 927-953.
7. J. W. BEBERNES, C. LI AND P. TALAGA, Single-point blow-up for non-local parabolic problems, Physica D, 134 (1999), 48-60.
8. M. BOHNER AND A. PETERSON, Dynamic Equations on Time Scales - An Introduction with Applications, Birkhäuser, Boston, 2001.
9. M. BOHNER AND A. PETERSON, Advances in Dynamic Equations on Time Scales, Birkhäuser Boston, Cambridge, MA, 2003.
10. E. CAGLIOTI, P-L. LIONS, C. MARCHIORO AND M. PULVIRENTI, A special class of stationary flows for two-dimensinal Euler equations: a statistical mechanics description, Comm. Math. Phys., 143 (1992), 501-525.
11. A. EL HACHIMI AND M.R. SIDI AMMI, Semidiscretization for a nonlocal parabolic problem, Int. J. Math. Math. Sci., 2005(10) (2005), 1655-1664.
12. A. EL HACHIMI, M.R. SIDI AMMI AND D.F.M. TORRES, A dual mesh method for a non-local thermistor problem, SIGMA Symmetry Integrability Geom. Methods Appl., 2 (2006), Paper 058, 10 pp. (electronic). [ONLINE: http://www.emis.de/journals/SIGMA/2006/Paper058/index.html]
13. D. GUO AND V. LAKSHMIKANTHAM, Nonlinear Problems in Abstract Cones, Academic press, Boston, 1988.
14. S. HILGER, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18-56.
15. S. HILGER, Differential and difference calculus-unified!, Nonlinear Anal., 30(5) (1997), 2683-2694.
16. M. A. KRASNOSELSKII, Positive Solutions of Operator Equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron, P. Noordhoff Ltd. Groningen, The Netherlands, 1964.
17. A. KRZYWICKI AND T. NADZIEJA, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat., 21(2) (1991), 265-272.
18. A.A. LACEY, Thermal runaway in a non-local problem modelling ohmic heating. Part I: Model derivation and some special cases, Euro. J. Appl. Math., 6 (1995), 127-144.
19. A.A. LACEY, Thermal runaway in a non-local problem modelling ohmic heating. Part II: General proof of blow-up and asymptotics of runaway, Euro. J. Appl. Math., 6 (1995), 201-224.
20. A.A. LACEY, Diffusion models with blow-up, J. Comp. Appl. Math., 97 (1998), 39-49.
21. D.-B. WANG, Existence, multiplicity and infinite solvability of positive solutions for p-Laplacian dynamic equations on time scales, Electron. J. Diff. Eqns., 2006(96) (2006), 1-10.
22. G. WOLANSKY, A critical parabolic estimate and application to non-local equations arising in chemotaxis, Appl. Anal., 66 (1997), 291-321.