Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
This paper is concerned with ground state solutions for the Hénon type equation [formula] in Ω, where Ω = Bk(0, 1) × Bn-k(0, 1) ⊂ Rn and x = (y, z) ∈ Rk × Rn-k. We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent [formula].
Czasopismo
Rocznik
Tom
Strony
411--424
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
autor
- Jiangxi Normal University Department of Mathematics Nanchang, Jiangxi 330022 People's Republic of China, hopelw@126.com
Bibliografia
- [1] M. Bhakta, K. Sandeep, Hardy-Sobolev-Maząŕya type equations in bounded domains, J. Differential Equations 247 (2009), 119–139.
- [2] D. Castorina, I. Fabbri, G. Mancini, K. Sandeep, Hardy-Sobolev inequalities, hyperbolic symmetry and the Webster scalar curvature problem, J. Differential Equations 246 (2009), 1187–1206.
- [3] D. Castorina, I. Fabbri, G. Mancini, K. Sandeep, Hardy-Sobolev inequalities and hyperbolic symmetry, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 3, 189–197.
- [4] D. Cao, S. Peng, The asymptotic behavior of the ground state solutions for Hénon equation, J. Math. Anal. Appl. 278 (2003), 1–17.
- [5] I. Fabbri, G. Mancini, K. Sandeep, Classification of solutions of a critical Hardy-Sobolev operator, J. Differential Equations 224 (2006) 2, 258–276.
- [6] B. Gidas, W.N. Ni, L. Nirenberg, Symmetries and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243.
- [7] B. Gidas, J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations 8 (1981), 883–901.
- [8] M. Hénon, Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys. 24 (1973), 229–238.
- [9] Q. Han, F.H. Lin, Elliptic Partial Differential Equations, AMS Providence, Rhode Island, 2000.
- [10] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin, 1983.
- [11] W.M. Ni, A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J 31 (1982), 801–807.
- [12] E. Serra, Non radial positive solutions for the Hénon equation with critical growth, Calc. Var. Partial Differential Equations 23 (2005) 3, 301–326.
- [13] D. Smets, J.B. Su, M. Willem, Non-radial ground states for the Hénon equation, Commun. Contemp. Math. 4 (2002), 467–480.
- [14] M. Willem, Minimax Theorems, Birkhäuser, Basel, 1996.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0005-0068
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