Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem

Journal of Differential Equations

Volumn 189, Issue 2, 2003, Pages 487-512

  Haitao, Yang ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Asymptotic behaviour; Critical exponent; Singular elliptic; Sub super solution

Indexed keywords

EID: 0037431219     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(02)00098-0     Document Type: Article

References (26)

1. R.P. Agarwal, D.O. Regan, Singular boundary value problems for superlinear second order ordinary and differential equations, J. Differential Equations 130 (1996) 333-355.
2. S. Alama, Semilinear elliptic equations with sublinear indefinite nonlinearities, Adv. in Differential Equations 4 (1999) 813-842.
3. A. Ambrosetti, J.G. Azorero, I. Peral, Multiplicity results for some nonlinear elliptic equations, J. Funct. Anal. 137 (1996) 219-242.
4. A. Ambrosetti, H. Brezis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994) 519-543.
5. M. Badiale, G. Tarantello, Existence and multiplicity results for elliptic problems with critical growth and discontinuous nonlinearities, Nonlinear Anal. Theory Methods Appl. 29 (1997) 639-677.
6. H. Brezis, E. Lieb, A relations between pointwise convergence of functions and convergence of integrals, Proc. Amer. Math. Soc. 88 (1983) 486-490.
7. H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equation involving the critical Sobolev exponent, Comm. Pure Appl. Math. 36 (1983) 437-477.
8. 1 local minimizers, C. R. Acad. Sci. Paris 317 (1993) 465-472.
9. H. Brezis, L. Oswald, Remarks on sublinear elliptic equation, Nonlinear Anal. Theory, Methods Appl. 10 (1986) 55-64.
10. M.M. Coclite, G. Palmieri, On a singular nonlinear Dirichlet problem, Comm. Partial Differential Equations 14 (1989) 1315-1327.
11. M.G. Crandall, P.H. Rabinowitz, L. Tartar, On a Dirichlet problem with a singular nonlinearity, Comm. Partial Differential Equations 2 (1977) 193-222.
12. A. Edelson, Entire solutions of singular elliptic equations, J. Math. Anal. Appl. 139 (1989) 523-532.
13. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer, Berlin, 1983.
14. A.V. Lair, A.W. Shaker, Classical and weak solutions of a singular semilinear elliptic problem, J. Math. Anal. Appl. 211 (1997) 371-385.
15. A.V. Lair, A.W. Shaker, Entire solution of a singular semilinear elliptic problem, J. Math. Anal. Appl. 200 (1996) 498-505.
16. A.C. Lazer, P.J. Mckenna, On a singular nonlinear elliptic boundary value problem, Proc. Amer. Math. Soc. 111 (1991) 721-730.
17. p as p→1, Comm. Partial Differential Equations 20 (1995) 633-646.
18. W.M. Ni, X.B. Pan, I. Takagi, Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J. 67 (1992) 1-20.
19. E.S. Noussair, J.F. Yang, On the existence of multiple positive solutions of critical semilinear elliptic problems, Nonlinear Anal. Theory, Methods Appl. 26 (1996) 1323-1346.
20. p = 0 on compact manifolds, Part II, Indiana Univ. Math. J. 40 (1991) 1083-1140.
21. A.W. Shaker, On singular semilinear elliptic equations, J. Math. Anal. Appl. 173 (1993) 222-228.
22. J. Shi, M. Yao, On a singular nonlinear elliptic problem, Proc. Roy. Soc. Edinburg Sect. A 128 (1998) 1389-1401.
23. M. Struwe, Variational Methods, Springer, Berlin, 1990.
24. Y.J. Sun, S.P. Wu, Y.M. Long, Combined effects of singular and superlinear nonlinearities in some singular boundary value problems, J. Differential Equations 176 (2001) 511-531.
25. G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992) 281-304.
26. Z.Q. Wang, The effect of the domain geometry on the number of positive solutions of Neumann problems with critical exponents, Differential Integral Equations 8 (1995) 1533-1554.