Multiple positive solutions for semilinear elliptic equations in ℝN involving critical exponents

Nonlinear Analysis, Theory, Methods and Applications

Volumn 34, Issue 4, 1998, Pages 593-615

  Alves, C O ^a   Goncalves, J V ^b   Miyagaki, O H ^c  

^a FEDERAL UNIVERSITY OF PARAÍBA   (Brazil)

^b UNIVERSITY OF BRASILIA   (Brazil)

^c FEDERAL UNIVERSITY OF VIÇOSA   (Brazil)

Author keywords

Critical exponents; Multiple positive solutions; Semilinear elliptic equations

Indexed keywords

INTEGRODIFFERENTIAL EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

SEMILINEAR ELLIPTIC EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0032210530     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00555-5     Document Type: Article

References (38)

1. W.A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Physics 55 (1977) 149-162.
2. H. Berestycki, P.L. Lions, Nonlinear scalar field equations - I, II, Arch. Rat. Mech. Anal. 82 (1983) 313-345, 347-375.
3. p on an unbounded symmetrical domain, Math. Ann. 263 (1983) 51-59.
4. N, Scuola Normale Superiore Pisa, 1991.
5. P.H. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew Math. Physics 43 (1992) 290-291.
6. P.L. Lions, The concentration-compactness principle in the calculus of variations - The limit case, I, II, Rev. Mat. Iberoamericana 1 (1985) 46-20, 145-201.
7. P.L. Lions, The concentration-compactness principle in the calculus of variations - The locally compact case, I, II, Ann. Inst. Henri Poincaré 1 (1984) 109-145, 223-283.
8. D.G. de Figueiredo, P.L. Lions, R.D. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures App. 61 (1982) 41-63.
9. M. Esteban, Nonlinear elliptic problems in strip-like domains, Nonlinear Analysis 7 (1983) 365-379.
10. G. Burton, Semilinear elliptic problems in unbounded domains, Math. Zeit. 190 (1985) 519-525.
11. H. Brézis, L. Nirenberg, Some variational problems with lack of compactness, Proc. Symp. Pure Math. (AMS) 45 (1986) 165-201.
12. N, Comm. Pure App. Math. XLV (1992) 1217-1269.
13. X.P. Zhu, H. Zhou, Existence of multiple positive solutions of inhomogenuous semilinear elliptic problems in unbounded domains, Proc. Royal Soc. Edinburgh 115A (1990) 301-318.
14. M. Struwe, Variational Methods: Applications to Differential Equations and Hamiltonian Systems, Springer, Berlin, 1990.
15. O. Kavian, Introduction à la théorie des points critiques et applications aux problems elliptiques, Springer, Berlin.
16. J.G. Azorero, I.P. Alonzo, Multiplicity of solutions for elliptic problems with critical exponents with a nonsymmetric term, Trans. Amer. Math. Society 323 (1991) 877-895.
17. G. Tarantello, On nonhomogeneous elliptic equations involving Sobolev exponent, Ann. Inst. Henri Poincaré 9 (1992) 281-304.
18. E.S. Noussair, C.A. Swanson, Y. Jianfu, Positive finite energy solutions of critical semilinear elliptic problems, Canadian J. Math. 44 (1992) 1014-1029.
19. D. Yinbing, Existence of multiple positive solutions for a semilinear equation with critical exponent, Proc. Royal Soc. Edinburgh 122A (1992) 161-175.
20. A. Ben-Naoum, C. Troestler, M. Willem, Extrema problems with critical Sobolev exponents on unbounded domains, Seminaire de Mathematique (Nouvelle Serie), Université Catholique de Louvain, Belgium.
21. n with critical growth, CMS Technical Report, Univ. of Winconsin, 1994.
22. N, J. Math. Anal. App. 172 (1993) 323-338.
23. N, J. Funct. Anal. 88 (1990) 90-117.
24. N with a non-Lipschitzian non-linearity, preprint.
25. X.P. Zhu, A perturbation result on positive entire solutions of a semilinear elliptic equation, J. Diff. Equations 92 (1991) 163-178.
26. A. Ambrosetti, H. Brézis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, preprint.
27. N involving subcritical exponents, Nonlinear Analysis, to appear.
28. W. Omana, M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Diff. Int. Equations 5 (1992) 1115-1120.
29. n, CMS Tech. Report, Univ. of Wisconsin, 1993.
30. J.V. Gonçalves, J.C. Pádua, P.C. Carrião, A note on sublinear elliptic problems on unbounded cylinders, J. Math. Anal. App., to appear.
31. H. Brézis, E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490.
32. J.V. Gonçalves, O.H. Miyagaki, Three solutions for a strongly resonant elliptic problem, Nonlinear Analysis 24 (1995) 265-272.
33. G. Talenti, Best constant in Sobolev inequality, Ann. Math. 110 (1976) 353-372.
34. T. Aubin, Problemes isoperimetriques et espaces de Sobolev, J. Diff. Geometry 11 (1976) 573-598.
35. J.L. Lions, Problèmes aux limits dans les équations aux dérivées partielles, Université de Montreal, 1965.
36. J. Chabrowski, On multiple solutions for the nonhomogeneous p-Laplacian with a critical Sobolev exponent, Diff. Integral Equations 8 (1995) 705-716.
37. H. Brézis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983) 437-477.
38. 2 with nonlinearities in the critical growth range, Cal. Var. PDE 3 (1995) 139-153.