Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents
Tóm tắt
Từ khóa
Tài liệu tham khảo
F. V. Atkinson, H. Brezis and L. A. Peletier,Nodal solutions of elliptic equations with critical Sobolev exponent, Journal of Differential Equations85 (1990), 151–170.
D. Cao and S. Peng,A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms, Journal of Differential Equations193 (2003), 424–434.
F. Catrina and Z. Wang,On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of external functions, Communications on Pure and Applied Mathematics54 (2001), 229–257.
G. Cerami, S. Solimini and M. Struwe,Some existence results for superlinear elliptic boundary value problems involing critical exponents, Journal of Functional Analysis69 (1986), 289–306.
K. Chou and C. Chu,On the best constant for a weighted Sobolev-Hardy inequality, Journal of the London Mathematical Society48 (1993), 137–151.
I. Ekeland and N. Ghoussoub,Selected new aspects of the calculus of variations in the large, Bulletin of the American Mathematical Society39 (2002), 207–265.
A. Ferrero and F. Gazzola,Existence of solutions for singular critical growth semilinear elliptic equations, Journal of Differential Equations177 (2001), 494–522.
J. P. Garcia Azorero and I. Peral. Alonso,Hardy inequalities and some critical elliptic and parabolic problems, Journal of Differential Equations144 (1998), 441–476.
N. Ghoussoub and C. Yuan,Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents, Transactions of the American Mathematical Society352 (2000), 5703–5743.
E. Jannelli,The role played by space dimension in elliptic critical problems, Journal of Differential Equations156 (1999), 407–426.
D. Kang and S. Peng,The existence of positive solutions and sign-changing solutions for elliptic equations with critical Sobolev-Hardy exponents, Applied Mathematics Letters17 (2004), 411–416.
P. L. Lions,The concentration compactness principle in the calculus of variations, the locally compact case (I), Annales de l'Institut Henri Poincaré. Analyse Non Linéaire1 (1984), 109–145.
P. L. Lions,The concentration compactness principle in the calculus of variations, the locally compact case (II), Annales de l'Institut Henri Poincaré. Analyse Non Linéaire1 (1984), 223–283.
P. L. Lions,The concentration compactness principle in the calculus of variations, the limit case (I), Revista Matemática Iberoamericana1 (1) (1985), 145–201.
P. L. Lions,The concentration compactness principle in the calculus of variations, the limit case (II), Revista Matemática Iberoamericana1 (2) (1985), 45–121.
D. Smets,Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities, Preprint of Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron 2, Belgium (2001).
G. Tarantello,Nodal solutions of semilinear elliptic equations with critical exponent, Differential and Integral Equations5 (1992), 25–42.
S. Terracini,On positive solutions to a class of equations with a singular coefficient and critical exponent, Advances in Differential Equations2 (1996), 241–264.