Existence theorems for elliptic equations involving supercritical sobolev exponent

Advances in Differential Equations

Volumn 2, Issue 2, 1997, Pages 231-256

  Chabrowski, J ^a   Yang, Jianfu ^b  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b NANCHANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84894542844     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Analysis 14 (1976), 349-381.
2. H. Berestycki and L.P. Lions, Nonlinear scalar field equations I, II, Arch. Rat. Mech. Anal. 82 (1983), 313-346, 283-308.
3. C. Budd and J. Norbury, Semilinear elliptic equations and supercritical growth, J. Diff. Equations 68 (1987), 169-197.
4. N, Ann. Inst. H. Poincaré, Analyse nonlinéaire 10(6) (1993), 593-604.
5. N with natural growth conditions, Proc. Roy. Soc. Edin. 113 A (1989), 215-228.
6. J. Chabrowski, Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponent, Calc. Var. PDE 3 (1995), 493-512.
7. W.Y. Ding and W.M. Ni, On the existence of positive entire solutions of semilinear elliptic equations, Arch. Rat. Mech. Anal. 91 (1986), 283-308.
8. I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-354.
9. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Heidelberg-New York-Tokyo, 1983.
10. Z. Jin, A truncation method for semilinear elliptic equations, Comm. PDE 19(3-4) (1994), 605-614.
11. N, Arch. Rat. Mech. Anal. 105 (1987), 243-266.
12. P.L. Lions, Symétrie et compacité dans les espaces de Sobolev, J. Funct. Analysis 49 (1982), 315-334.
13. F. Merle and L.A. Peletier, Asymptotic behaviour of positive solutions of elliptic equations with critical and subcritical growth I. The Radial Case, Arch. Rat. Mech. Anal. 112 (1990), 1-19.
14. F. Merle and L. A. Peletier, Positive solutions of elliptic equations involving supercritical growth, Proc. Roy. Soc. Edin. 118 A (1991), 49-63.
15. F. Merle, L.A. Peletier and J. Serrin, A bifurcation problem at a singular limit, Indiana Univ. Math. J 43(2) (1994), 585-609.
16. D. Passaseo, Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1993), 97-105.
17. S. Pohozaev, Eigenfunctions of the equation δu + λf(u) = 0, Soviet. Math. Doklady 6 (1965), 1408-1411.
18. S. Pohozaev, Elliptic problems with supercritical nonlinearity, Russian, Mat. Sb. 182(4) (1991), 467-489.
19. P. H. Rabinowitz, Variational methods for nonlinear elliptic eigenvalue problems, Indiana Univ. J. Maths. 23 (1974), 729-754.
20. M. Struwe, Variational Methods, Springer-Verlag, Berlin-Heidelberg, 1990.
21. N) for a semilinear elliptic equation, Proc. London Math. Soc. 3(37) (1988), 511-541.
22. Xiaomin Zheng, Un résultat de non-existence de solution positve pour une équation elliptique, Ann. Inst. H. Poincaré, Analyse nonlinéaire 7(2) (1990), 91-96.
23. Jianfu Yang and Xiping Zhu, On the existence of nontrivial solution of a quasilinear elliptic boundary value problem for unbounded domains (1) Positive mass case, (2) Zero mass case, Acta Math. Scientia 7(3-4) (1987), 341-359, 447-459.