Positive solution of singular Dirichlet boundary value problems for second order differential equation system

Journal of Mathematical Analysis and Applications

Volumn 328, Issue 2, 2007, Pages 1255-1267

  Wei, Zhongli ^a,b  

^a SHANDONG JIANZHU UNIVERSITY   (China)

^b SHANDONG UNIVERSITY   (China)

Author keywords

Differential system; Lower and upper solutions; Positive solution; Singular Dirichlet boundary value problem

Indexed keywords

EID: 33845907386     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.06.053     Document Type: Article

References (24)

1. O'Regan D. Theory of Singular Boundary Value Problems (1994), World Scientific Press, Singapore
2. Taliaferro S.D. A nonlinear singular boundary value problem. Nonlinear Anal. 3 6 (1979) 897-904
3. Zhang Y. Positive solutions of singular sublinear Emden-Fowler boundary value problems. J. Math. Anal. Appl. 185 1 (1994) 215-222
4. O'Regan D. Singular Dirichlet boundary value problems I. Superlinear and nonresonance case. Nonlinear Anal. 29 2 (1997) 221-249
5. Shaozhu C., and Yong Z. Singular boundary value problems on a half-line. J. Math. Anal. Appl. 195 2 (1995) 449-468
6. Wei Z. Positive solutions of singular boundary value problems of negative exponent Emden-Fowler equations. Acta Math. Sinica 41 3 (1998) 655-662 (in Chinese)
7. Dunning D.R., and Wang H. Existence and multiplicity of positive solutions for elliptic systems. Nonlinear Anal. 29 (1997) 1051-1060
8. Dunning D.R., and Wang H. Multiplicity of positive radial solutions for an elliptic system on an annulus domain. Nonlinear Anal. 42 (2000) 803-811
9. Lee Y.-H. Multiplicity of positive radial solutions for multi-parameter semilinear elliptic systems on an annulus. J. Differential Equations 174 (2001) 420-441
10. Fink A.M., and Gatica J.A. Positive solutions of second order systems of boundary value problems. J. Math. Anal. Appl. 180 (1993) 93-108
11. Ma R. Existence of positive radial solutions for elliptic systems. J. Math. Anal. Appl. 201 (1996) 375-386
12. Ma R. Multiple nonnegative solutions of second order systems of boundary value problems. Nonlinear Anal. 42 (2000) 1003-1010
13. Liu X., and Sun J. Computation of topological degree and applications to suplinear systems of equations. J. Systems Sci. Math. Sci. 16 1 (1996) 51-59 (in Chinese)
14. Zhang Z. Existence of nontrivial solution for super-linear system of integral equations and its applications. Acta Math. Appl. Sin. 15 2 (1999) 153-162
15. Coclite M.M., and Palmieri G. On a singular nonlinear Dirichlet problem. Comm. Partial Differential Equations 14 (1989) 1315-1327
16. Crandall M.G., Rabinowitz P.H., and Tartar L. On a Dirichlet problem with a singular nonlinearity. Comm. Partial Differential Equations 2 (1977) 193-222
17. Cui S. Existence and nonexistence of positive solutions for singular semilinear elliptic boundary value problems. Nonlinear Anal. 41 (2000) 149-176
18. Ghergu M., and Řadulescu V. Sublinear singular elliptic problems with two parameters. J. Differential Equations 195 (2003) 520-536
19. Gomes S.M. On a singular nonlinear elliptic problem. SIAM J. Math. Anal. 17 (1986) 1359-1369
20. Lazer A.C., and McKenna P.J. On a singular elliptic boundary value problem. Proc. Amer. Math. Soc. 111 (1991) 721-730
21. Magli H., and Zribi M. Existence and estimates of solutions for singular nonlinear elliptic problems. J. Math. Anal. Appl. 263 (2001) 522-542
22. Shi J., and Yao M. On a singular semilinear elliptic problem. Proc. Roy. Soc. Edinburgh Sect. A Math. 128 (1998) 1389-1401
23. Zhang Z. The asymptotic behaviour of the unique solution for the singular Lane-Emden-Fowler equation. J. Math. Anal. Appl. 312 (2005) 33-43
24. Hartman P. Ordinary Differential Equations. second ed. (1982), Birkhäuser, Boston