On a class of semilinear elliptic problems in double-struck R signN with critical growth

Nonlinear Analysis, Theory, Methods and Applications

Volumn 29, Issue 7, 1997, Pages 773-781

  Miyagaki, Olimpio Hiroshi ^a  

^a FEDERAL UNIVERSITY OF VIÇOSA   (Brazil)

Author keywords

Critical Sobolev exponents and Mountain Pass Theorem; Palais Smale condition; Variational methods

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; NONLINEAR EQUATIONS; THEOREM PROVING; VARIATIONAL TECHNIQUES;

CRITICAL SOBOLEV EXPONENTS; MOUNTAIN PASO THEOREM; PALAIS-SMALE CONDITION; SEMILINEAR ELLIPTIC PROBLEMS;

PROBLEM SOLVING;

EID: 0031258707     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00087-9     Document Type: Article

References (32)

1. Brezis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Communs pure appl. Math., 1983, 36, 437-477.
2. Atkinson, F. V. and Peletier, L. A., Emden-Fowler equations involving critical exponents. Nonlinear Analysis, 1986, 10, 755-776.
3. 2*-2. Manuscripta math., 1986, 54, 373-379.
4. Capozzi, A., Fortunato, D. and Palmieri, G., An existence result for nonlinear elliptic problems involving critical Sobolev exponent. Ann. Inst. H. Poincaré Analyse non Linéaire, 1985, 2(6), 463-470.
5. Cerami, G., Fortunato, D. and Struwe, M., Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents. Ann Inst. H. Poincaré Analyse non Linéaire, 1984, 1(5), 341-350.
6. Cerami, G., Solimini, S. and Struwe, M., Some existence results for superlinear elliptic boundary value problems involving critical exponents. J. funct. Analysis, 1986, 69, 289-306.
7. Dancer, E. N., A note on an equation with critical exponent. Bull. London math. Soc., 1988, 20, 600-602.
8. (n+2)/(n+2) = 0 and related topics. Duke math. J., 1985, 52, 485-506.
9. Pohozaev, S. I., Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl., 1965, 6, 1408-1411.
10. Azorero, J. G. and Alonso, I. P., Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term. Trans. Am. math. Soc., 1991, 323(2), 877-895.
11. Egnell, H., Existence and nonexistence results for m-Laplace equations involving critical Sobolevc exponents. Arch. ration. Mech. Analysis, 1988, 104, 57-77.
12. Guedda, M. and Veron, L., Quasilinear elliptic equations involving critical Sobolev exponents. Nonlinear Analysis, 1989, 13(8), 879-902.
13. N. J. funct. Analysis, 1990, 80, 90-117.
14. Noussair, E. S., Swanson, C. A. and Jianfu, Y., Positive finite energy solutions of critical semilinear elliptic problems. Can. J. Math., 1992, 44(5), 1014-1029.
15. n and in balls. J. math. Analysis Applic., 1993, 172, 323-338.
16. Kabeya, Y., On some quasilinear elliptic problems involving critical Sobolev exponents. Funkcialaj Ekvacioj, 1993, 36, 385-404.
17. Noussair, E. S., Swanson, C. A. and Jianfu, Y., Quasilinear elliptic problems with critical exponents. Nonlinear Analysis, 1993, 20(3), 285-301.
18. Xiping, Z. and Jianfu, Y., The quasilinear elliptic equations on unbounded domain involving critical Sobolev exponent. J. Partial Differential Equations, 1989, 2(2), 53-64.
19. Rabinowitz, P. H., On a class of nonlinear Schrödinger equations. Z. angew Math. Phys (Zamp), 1992, 43, 270-291.
20. N. CMS Tech. Sum. Rep., 1993, 93-13.
21. Brezis, H., Nonlinear elliptic equations involving the critical Sobolev exponent: survey and perspectives. In Directions in Partial Differential Equations, ed. M. G. Crandall, P. H. Rabinowitz and R. E. L. Turner. Academic Press, 1987, pp. 17-36.
22. Omana, W. and Willem, M., Homoclinic orbits for a class of Hamiltonian systems. Differential and Integral Equations, 1992, 5(5), 1115-1120.
23. Ambrosetti, A. and Rabinowitz, P. H., Dual variational methods in critical point theory and applications. J. funct. Analysis, 1973, 14, 349-381.
24. Aubin, T. and Ekeland, I., Applied Nonlinear Analysis. Wiley, 1984.
25. Brezis, H. and Nirenberg, L., Remarks on finding critical points. Communs pure appl. Math., 1991, 44, 939-963.
26. de Figueiredo, D. G., Lectures on the Ekeland Principle with Applications and Detours. Springer, 1980.
27. Mawhin, J. and Willem, M., Critical Point Theory and Hamiltonian Systems. Springer, 1989.
28. Brezis, H. and Kato, T., Remarks on the Schrödinger operator with singular complex potential. J. Math. pures appl., 1979, 58, 137-151.
29. Berestycki, H. and Lions, P.-L., Nonlinear scalar field equations - I. Existence of a ground state. Arch. ration. Mech. Analysis, 1983, 82(4), 313-345.
30. n. Communs pure appl. Math., 1992, 45, 1217-1269.
31. Rabinowitz, P. H., Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Regional Conf. Ser. in Math. 65, AMS, Providence, RI, 1986.
32. Talenti, G., Best constants in Sobolev inequality. Annali Mat. pura appl., 1976, 110, 353-372.