Semilinear Neumann problem in exterior domains

Nonlinear Analysis, Theory, Methods and Applications

Volumn 31, Issue 7, 1998, Pages 791-821

  Pan, Xing Bin ^a   Wang, Xuefeng ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b Tulane University   (United States)

Author keywords

Asymptotic behavior; Critical Sobolev exponents; Elliptic equations; Energy; Existence

Indexed keywords

ASYMPTOTIC STABILITY; PROBLEM SOLVING; THEOREM PROVING;

LEAST ENERGY SOLUTIONS; SEMILINEAR NEUMANN EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0032017262     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00440-9     Document Type: Article

References (26)

1. Lin, C.-S. and Ni, W.-M., On the diffusion coefficient of a semilinear Neumann problem. Calculus of Variations and Partial Differential Equations, ed. S. Hildebrandt, D. Kinderlehrer and M. Miranda. Lecture Notes in Math. 1340. Springer-Verlag, 1988, pp. 160-174.
2. Lin, C.-S., Ni, W.-M. and Takagi, I., Large amplitude stationary solutions to a chemotaxis system. J. Diff. Eqns., 1988, 72, 1-27.
3. Ni, W.-M. and Takagi, I., On the shape of least-energy solutions to a semilinear Neumann problem. Commun. Pure Appl. Math., 1991, 44, 819-851.
4. Ni, W.-M. and Takagi, I., Locating the peaks of least energy solutions to a semilinear Neumann problem. Duke Math. J., 1993, 72, 247-281.
5. Ni, W.-M. and Takagi, I., On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type. Trans. Amer. Math. Soc., 1986, 297, 251-368.
6. Ni, W.-M., Pan, X.-B. and Takagi, I., Singular behavior of least-energy solutions of a semilinear Neumann problem involving Critical Sobolev exponents. Duke Math. J., 1992, 67, 1-20.
7. Adimurthi and Mancini, G., The Neumann problem for elliptic equations with critical nonlinearity. Scuola Norm. Sup. Pisa, 1991, 9-25.
8. Wang, X.-J., Neumann problem of semilinear elliptic equations involving critical Sobolev exponents. J. Diff. Eqns., 1991, 93, 283-310.
9. Esteban, M., Nonsymmetric ground states of symmetric variational problems. Comm. Pure Appl. Math., 1991, 44, 259-274.
10. Wang, Z.-Q., On the existence of positive solutions for semilinear Neumann problems in exterior domains. Comm. in P.D.E., 1992, 17, 1309-1325.
11. Pan, X.-B., Condensation of least-energy solutions of a semilinear Neumann problem. J. P.D.E., 1995, 8, 1-36.
12. Pan, X.-B., Condensation of least-energy solutions: the effect of boundary conditions. Nonlinear Analysis, 1995, 24, 195-222.
13. Pan, X.-B. and Xu, X.-W., Least energy solutions of semilinear Neumann problems and asymptotics. JMAA, 1996, 201, 532-554.
14. Adimurthi, Pacella, F. and Yadava, S. L., Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity. J. Functional Anal., 1993, 113, 318-350.
15. Brezis, H. and Nirenberg, L., Positive solution of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math., 1983, 36, 437-477.
16. Talenti, G., Best constant in Sobolev inequalities. Ann. Mat. Pura Appl., 1976, 110, 697-718.
17. Brezis, H. and Lieb, E., A relation between pointwise convergence of functions and weak convergence of functionals. Proc. Amer. Math. Soc., 1983, 88, 436-477.
18. Adams, R., Sobolev Spaces. Academic Press, Boston, 1978.
19. Caffarelli, L., Gidas, B. and Spruck, J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math., 1989, 42, 271-297.
20. Chen, W. and Li, C., Classification of solutions of some nonlinear elliptic equations. Duke Math. J., 1991, 63, 615-622.
21. Escobar, J., Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary. Ann. of Math., 1992, 136, 1-50.
22. Bahri, A., Critical points at infinity in some variational problems. Pitman Research Notes in Mathematics Series, Vol. 182. Wiley, 1989.
23. Bianchi, G. and Egnell, H., A note on the Sobolev inequality. J. Functional Anal., 1991, 100, 18-24.
24. Pan, X.-B., Further study of the effect of boundary conditions. J. Diff. Eqns., 1995, 117, 446-468.
25. n involving critical Sobolev exponent. J. Diff. Eqns., 1992, 99, 78-107.
26. n. Advances in Math. Supplementary Studies, 7A. Academic, New York, 1981, pp. 369-402.