Multiple positive solutions of singular Dirichlet problems on time scales via variational methods

Nonlinear Analysis, Theory, Methods and Applications

Volumn 67, Issue 2, 2007, Pages 368-381

  Agarwal, Ravi P ^a   Otero Espinar, Victoria ^b   Perera, Kanishka ^a   Vivero, Dolores R ^b  

^a Florida Institute of Technology ^*  (United States)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Critical point theory; Dynamic boundary value problem; Multiple positive solutions; Singular; Variational methods

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; VARIATIONAL TECHNIQUES;

CRITICAL POINT THEORY; DYNAMIC BOUNDARY VALUE PROBLEM; MULTIPLE POSITIVE SOLUTIONS; VARIATIONAL METHODS;

BOUNDARY VALUE PROBLEMS;

EID: 34047256840     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.05.014     Document Type: Article

References (14)

1. Agarwal R.P., and O'Regan D. Singular Differential and Integral Equations with Applications (2003), Kluwer Academic Publishers, Dordrecht
2. Agarwal R.P., O'Regan D., and Wong P.J.Y. Positive Solutions of Differential, Difference and Integral Equations (1999), Kluwer Academic Publishers, Dordrecht
3. Agarwal R.P., Otero-Espinar V., Perera K., and Vivero D.R. Basic properties of Sobolev spaces on time scales. Adv. Difference Equ. 2006 (2006) 14 pages. Article ID 38121
4. R.P. Agarwal, V. Otero-Espinar, K. Perera, D.R. Vivero, Wirtinger's inequalities on time scales, Canad. Math. Bull. (in press)
5. Agarwal R.P., Perera K., and O'Regan D. Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Anal. 58 (2004) 69-73
6. Agarwal R.P., Perera K., and O'Regan D. Multiple positive solutions of singular problems by variational methods. Proc. Amer. Math. Soc. 134 3 (2006) 817-824
7. Bohner M., and Peterson A. Advances in Dynamic Equations on Time Scales (2003), Birkhäuser Boston, Inc., Boston, MA
8. Cabada A., and Vivero D.R. Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral. Application to the calculus of Δ-antiderivatives. Math. Comput. Modelling 43 (2006) 194-207
9. Cabada A., and Vivero D.R. Criterions for Absolutely Continuity on Time Scales. J. Difference Equ. Appl. 11 11 (2005) 1013-1028
10. Cerami G. An existence criterion for the critical points on unbounded manifolds. Istit. Lombardo Accad. Sci. Lett. Rend. A 112 2 (1979) 332-336 1978
11. Guseinov G.Sh. Integration on time scales. J. Math. Anal. Appl. 285 1 (2003) 107-127
12. Hewitt E., and Stromberg K.R. Real and Abstract Analysis. third ed. (1975), Springer-Verlag, New York
13. Rabinowitz P.H. Minimax methods in critical point theory with apinimax methods in critical point theory with applications to differential equations. CBMS Regional Conference Series in Mathematics vol. 65 (1986), Conference Board of the Mathematical Sciences, Washington, DC
14. Rudin W. Real and Complex Analysis. third ed. (1987), McGraw-Hill Book Co., New York (First ed. McGraw-Hill Book Co., 1966)