Existence of two solutions of nonlinear elliptic equations with critical Sobolev exponents and mixed boundary conditions

Royal Society of Edinburgh - Proceedings A

Volumn 126, Issue 1, 1996, Pages 47-75

  Huang, Feimin ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

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[No Author keywords available]

Indexed keywords

EID: 33646110824     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500030596     Document Type: Article

References (16)

1. H. Brezis and L. Nirenberg. Positive solution of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure. Appl. Math. 36 (1983), 436-77.
2. H. Brezis and L. Nirenberg. A minimization problem with critical exponent and non zero data. In Symmetry in Nature, 129-40 (Pisa: Scuola Normale Superiore, 1989).
3. n. Proc. Roy. Soc. Edinburgh Sect. A (to appear).
4. J. M. Coron. Topologist et cas limite des injections de Sobolev. C. R. Acad. Sci. Paris Ser. I 299 (1984), 209-12.
5. I. Ekeland. Non-convex minimization problems. Bull. Amer. Math. Soc. 1 (1979), 443-74.
6. J. G. Eagle. Monotone method for semilinear elliptic equations in unbounded domains. J. Math. Anal. Appl. 137 (1989), 122-31.
7. M. Grossi. On some semilinear elliptic equations with critical nonlinearities and mixed boundary conditions. Rend. Mat. Ser. VIII 10 (1990), 287-302.
8. M. Grossi. Existence and multiplicity results in the presence of symmetry for elliptic equations with critical Sobolev exponent. Nonlinear Anal. 17 (1991), 973-89.
9. M. Grossi and F. Pacella. Positive solution of nonlinear elliptic equation with critical Sobolev exponent and mixed boundary condition. Proc. Roy. Soc. Edinburgh Sect. A 116 (1990), 23-43.
10. P. L. Lions, F. Pacella and M. Tricarico. Best constant in Sobolev inequalities for functions vanishing on some part of the boundary and related questions. Indiana Univ. Math. J. 2 (1988), 301-24.
11. F. Pacella and M. Tricarico. Symmetrization for a class of elliptic equations with mixed boundary conditions. Atti. Sem. Mat. Fis. Univ. Modena 34 (1986), 75-94.
12. D. Passaseo. Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains. Manscripta Math. 2 (1989), 147-65.
13. S. I. Pohozaev. Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl. 6 (1976), 1408-11;
14. translated from the Russian Dokl. Akad. Nauk. SSSR 65 (1965), 33-6.
15. G. Tarantello. On nonhomogeneous elliptic equations involving critical Sobolev exponent. Ann. Inst. H. Poincaré Anal. Non Lineaire 9 (1992), 281-304.
16. X. J. Wang. Neuman problems of semilinear elliptic equations involving critical Sobolev exponents. J. Differential Equations 93 (1991), 283-310.