Positive solutions of certain elliptic equations involving critical Sobolev exponents

Nonlinear Analysis, Theory, Methods and Applications

Volumn 33, Issue 6, 1998, Pages 617-636

  Huang, Yin Xi ^a  

^a University of Memphis   (United States)

Author keywords

Critical Sobolev exponent; Multiple positive solutions; The p Laplacian

Indexed keywords

BOUNDARY CONDITIONS; INTEGRAL EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

CRITICAL SOBOLEV EXPONENT; LAPLACE EQUATIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032166767     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00671-8     Document Type: Article

References (25)

1. N with critical growth, preprint.
2. A. Ambrosetti, H. Brezis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994) 519-543.
3. A. Ambrosetti, J.G. Azorero, I. Peral, Multiplicity results for some nonlinear elliptic equations, J. Funct. Anal. 137 (1996) 219-242.
4. J.G. Azorero, I.P. Alonso, Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term, Trans. Amer. Math. Soc. 323 (1991) 877-895.
5. J.G. Azorero, I.P. Alonso, Some results about the existence of a second positive solution in a quasilinear critical problem, Ind. Univ. Math. J. 43 (1994) 941-957.
6. J.G. Azorero, I.P. Alonso, J.P. Puel, Quasilinear problems with exponential growth in the reaction term, Nonlinear Anal. 22 (1994) 481-498.
7. T. Bartsch, M. Willem, On an elliptic equation with concave and convex nonlinearities, Proc. Amer. Math. Soc. 123 (1995) 3555-3561.
8. L. Boccardo, M. Escobedo, I. Peral, A Dirichlet problem involving critical exponents, Nonlinear Anal. 24 (1995) 1639-1648.
9. H. Brezis, E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490.
10. X. Cabré, P. Majer, Truncation of nonlinearities in some supercritical elliptic problems, C.R. Acad. Sci. Paris 322, Ser I (1996) 1157-1162.
11. A. Castro, Y.X. Huang, Structure of the set of positive radial solutions of a p-Laplacian equation including the critical exponent case, preprint.
12. N with critical Sobolev exponent, J. Diff. Equip. 140 (1997) 106-132.
13. N. Ghoussoub, Duality and Perturbation Methods in Critical Point Theory, Cambridge University Press, London, 1993.
14. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, New York, 1983.
15. Y.X. Huang, Existence of positive solutions for a class of the p-Laplacian equations, J. Austral. Math. Soc. Ser. B. 36 (1994) 249-264.
16. B. Kawohl, On a family of torsional creep problems, J. Reine Angew. Math. 410 (1990) 1-22.
17. P.L. Lions, The concentration-compactness principle in the calculus of variations, the limit case, Part I, II, Rev. Mat. Iber. 1 (2, 3) (1985) 109-145, 45-121.
18. R. Ma, On a conjecture concerning the multiplicity of positive solutions of elliptic problems, Nonlinear Anal. 27 (1996) 775-780.
19. M. Otani, T. Teshima, On the first eigenvalue of some quasilinear elliptic equations, Proc. Japan Acad. Ser. A 64 (1988) 8-10.
20. S. Sakaguchi, Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems, Ann. Sc. Norm. Sup. Pisa 14 (1987) 403-421.
21. G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent, Ann. I.H.P. Anal, non Linéaire 9 (1992) 281-304.
22. N.S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations, Comm. Pure Appl. Math. 20 (1967) 721-747.
23. Wei Zhihui, Wu Xinmin, A multiplicity result for quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. 18 (1992) 559-567.
24. J. Yang, Positive solutions of quasilinear elliptic obstacle problems with critical exponents, Nonlinear Anal. 25 (1995) 1283-1306.
25. X. Zhu, Nontrivial solution of quasilinear elliptic equations involving critical Sobolev exponent, Sci. Sinica, Ser. A 31 (1988) 1166-1181.