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Warianty tytułu
Języki publikacji
Abstrakty
We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: (i) 2 < p+1 <2*s, (ii) p+1 = 2*(s) and (iii) 2*(s) < p+1 ≤ 2*, where [formula] denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.
Czasopismo
Rocznik
Tom
Strony
271--290
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- University of Queensland Department of Mathematics St. Lucia 4072, Qld, Australia
Bibliografia
- [1] Adimurthi, G. Mancini, The Neumann problem for elliptic equations with critical nonlinearity, A tribute in honour of G. Prodi, Scuola Norm. Sup. Pisa (1991), 9–25.
- [2] Adimurthi, G. Mancini, Effect of geometry and topology of the boundary in critical Neumann problem, J. Reine Angew. Math. 456 (1994), 1–18.
- [3] A. Ambrosetti, P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349–381.
- [4] T. Bartsch, Zhi-Qiang Wang, M. Willem, The Dirichlet problem for superlinear elliptic equations, Handbook of Differential Equations, M. Chipot and P. Quittner (eds.), Elsevier B.V., 2005.
- [5] H. Berestycki, I. Capuzzo-Dolcetta, L. Nirenberg, Variational methods for indefinite superlinear homogeneous elliptic problems, NoDEA 2 (1995), 553–572.
- [6] H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Commun. Pure and Appl. Mathematics XXXVI (1983), 437–477.
- [7] D. Cao, J. Chabrowski, Critical Neumann problem with competing Hardy potentials,Rev. Mat. Complut. 20 (2007), 309–338.
- [8] J. Chabrowski, M. Willem, Least energy solutions of a critical Neumann problem with weight, Calc. Var. 15 (2002), 421–431.
- [9] J. Chabrowski, On the Neumann problem involving the Hardy-Sobolev potentials, Annals of the University of Bucharest (Mathematical Series) 1 (LIX) (2010), 211–228.
- [10] J. Chabrowski, On the Neumann problem with with the Hardy-Sobolev potential, Ann.Math. Pura Appl. 186 (2007), 703–719.
- [11] J. Chabrowski, The Neumann problem for semilinear elliptic equations with critical Sobolev exponent, Milan J. Mathematics 75 (2007), 197–224.
- [12] J. Chabrowski, On the Neumann problem with multiple critical nonlinearities, Complex Variables and Elliptic Equations 55 (2010) 5–6, 501–524.
- [13] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324–353.
- [14] D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations, 2nd ed.,Springer-Verlag, Berlin Heidelberg New York Tokyo, 1983.
- [15] N. Ghoussoub, C. Yuan, Multiple solutions for quasilinear PDEs involving the critical Sobolev exponents, Trans. Am. Math. Soc. 88 (2000), 5703–5743.
- [16] N. Ghoussoub, X.S. Kang, Hardy-Sobolev critical elliptic equations with boundary singularities, Ann. Inst. H. Poincaré Analysis Non Linéaire 21 (2004), 767–793.
- [17] Chu-Hsiung Hsia, Chang-Shou Lin, Hidemisu Wadade, Revisiting an idea of Brézis and Nirenberg, J. Funct. Anal. (2010), doi:10(16)jfa.2010.05.004
- [18] P.L. Lions, The concentration-compactness principle in the calculus of variations, The limit case. Parts 1,2, Rev. Mat. Iberoamericana 1 (1985) 1, 145–201 and no. 2, 45–121.
- [19] J.D. Rossi, Elliptic problems with nonlinear boundary conditions and the Sobolev trace theorem, Handbook of Differential Equations, M. Chipot and P. Quittner (eds.), Elsevier P.V., 2005.
- [20] M. Struwe, Variational methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer, 1996.
- [21] G. Talenti, Best constants in Sobolev inequality, Ann. Math. Pura Appl. 110 (1976), 353–372.
- [22] G. Tarantello, Multiplicity results for an inhomogeneous Neumann problem with critical exponent, Manuscripta Math. 81 (1993) 1, 57–78.
- [23] X.J. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponent, J. Diff. Equations 93 (1991), 283–310.
- [24] M. Willem, Min-max Theorems, Birkhäuser, Boston, 1996.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-423f26a2-e25d-4758-96ac-37f427140c78