Problem with Critical Sobolev Exponent and with Weight

Ambrosetti, A. and Rabinowitz, P., Dual variational methods in critical point theory and applications, J. Funct. Anal., 14, 1973, 349–381

Bahri, A. and Coron, J. M., On a nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain, Comm. Pure Appl. Math., 41, 1988, 253–294

Brezis, H., Elliptic equations with limiting Sobolev exponents, The impact of topology, Comm. Pure Appl. Math., 39, 1986, S17–S39

Brezis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36, 1983, 437–477

Brezis, H. and Lieb, E., A relation between pointwise convergence of functions and convergence of func- tionals, Proc. Amer. Math. Soc., 88, 1983, 486–490

Coron, J. M., Topologie et cas limite des injections de Sobolev, C. R. Acad. Sc., Paris., 299, 1985, 209–211

Caffarelli, L., Kohn, R. and Nirenberg, L., First order interpolation inequalities with weights, Compositio Math., 53, 1984, 259–275

Dancer, E. N., A note on an equation with critical exponent, Bull. London Math. Soc., 20(6), 1988, 600–602

Ding, W. Y., Positive solutions of Δu + u (n+2)/(n−2) = 0 on contractible domains, J. Partial Differential Equations, 2(4), 1989, 83–88

Hadiji, R., Solutions positives de l'equation −Δu = u p +μu q dans un domaine àtrou, Annales de la Faculté des Sciences de Toulouse, XI(3), 1990, 55–71

Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities, Cambridge University Press, Cambridge, 1952

Lions, P. L., The concentration-compactness principle in the calculus of variations, The limit case, part 1, Rev. Mat. Iberoamericana, 1(1), 1985, 145–201

Lewandowski, R., Little holes and convergence of solutions of −Δu = u (N+2)/(N−2) , Nonlinear Analysis, Theory, Methods and Applications, 14(10), 1990, 873–888

Passaseo, D., Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math., 65(2), 1989, 147–165

Pohozaev, R. S. J., Eigenfunctions of the equation Δu + λf(u) = 0, Soviet Math. Doklady, 6, 1965, 1408–1411

Struwe, M., A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z., 187, 1984, 511–517