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Lawrence Sirovich (1941)
Partial Differential Equations
B. Abdellaoui, E. Colorado, I. Peral (2004)
Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalitiesJournal of the European Mathematical Society, 6
Xu-jia Wang (1991)
Neumann problems of semilinear elliptic equations involving critical Sobolev exponentsJournal of Differential Equations, 93
J. Lions, R. Dautray, P. Bénilan (1990)
Mathematical Analysis and Numerical Methods for Science and Technology: Volume 1 Physical Origins and Classical Methods
Paris Vz
Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents Haim Brezis
R. Dautray, J. Lions, C. DeWitt-Morette, E. Myers (1990)
Mathematical Analysis and Numerical Methods for Science and TechnologyPhysics Today, 44
Florin Catrina, Zhi-Qiang Wang (2001)
On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions †Communications on Pure and Applied Mathematics, 54
N. Ghoussoub, C. Yuan (2000)
Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponentsTransactions of the American Mathematical Society, 352
S. Terracini (1996)
On positive entire solutions to a class of equations with a singular coefficient and critical exponentAdvances in Differential Equations
L. Caffarelli, R. Kohn, L. Nirenberg (1984)
First order interpolation inequalities with weightsCompositio Mathematica, 53
B. Abdellaoui, E. Colorado, I. Peral (2005)
Some improved Caffarelli-Kohn-Nirenberg inequalitiesCalculus of Variations and Partial Differential Equations, 23
M. Willem (1996)
Minimax theorems. Progress in nonlinear Differential Equations and their Applications, 24
T. Bartsch, Shuangjie Peng, Zhitao Zhang (2007)
Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalitiesCalculus of Variations and Partial Differential Equations, 30
A. Dall'Aglio, D. Giachetti, I. Alonso (2005)
Results on Parabolic Equations Related to Some Caffarelli-Kohn-Nirenberg InequalitiesSIAM J. Math. Anal., 36
T. Horiuchi (1997)
Best Constant in Weighted Sobolev Inequality with Weights Being Powers of Distance from the OriginJournal of Inequalities and Applications, 1
P. Cherrier (1984)
Problèmes de Neumann non linéaires sur les variétés riemanniennesJournal of Functional Analysis, 57
M. Willem (1997)
Minimax Theorems
N. Ghoussoub, X. Kang (2004)
Hardy-Sobolev critical elliptic equations with boundary singularitiesAnn. Inst. H. Poincaré Anal. Non Linéaire, 21
P. Han, Zhaoxia Liu (2003)
Positive solutions for elliptic equations involving critical Sobolev exponents and Hardy terms with Neumann boundary conditionsNonlinear Analysis-theory Methods & Applications, 55
D. Pierotti, S. Terracini (1995)
On a Neumann problem with critical exponent and critical nonlinearity on the boundaryCommunications in Partial Differential Equations, 20
D. Cao, Shuangjie Peng (2003)
A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms $Journal of Differential Equations, 193
D. Smets (2005)
Nonlinear Schrödinger equations with Hardy potential and critical nonlinearitiesTransactions of the American Mathematical Society, 357
Adimurthi, S. Yadava (1990)
Critical sobolev exponent problem in ℝn(n ≥ 4) with neumann boundary conditionProceedings of the Indian Academy of Sciences - Mathematical Sciences, 100
D. Cao, Shuangjie Peng (2002)
A global compactness result for singular elliptic problems involving critical Sobolev exponent, 131
A. Adimurthi, F. Pacella, S. Yadava (1993)
Interaction between the Geometry of the Boundary and Positive Solutions of a Semilinear Neumann Problem with Critical NonlinearityJournal of Functional Analysis, 113
N. Ghoussoub, X. Kang (2004)
Hardy–Sobolev critical elliptic equations with boundary singularitiesAnnales De L Institut Henri Poincare-analyse Non Lineaire, 21
J. Chabrowski (2004)
On the nonlinear Neumann problem involving the critical Sobolev exponent and Hardy potential.Revista Matematica Complutense, 17
H. Brezis, L. Nirenberg (1983)
Positive solutions of nonlinear elliptic equations involving critica sobolve exponentsComm. Pure Appl. Math., 36
Let Ω be a bounded domain with a smooth C 2 boundary in ℝ N (N ≥ 3), 0 ∈ $$ \bar \Omega $$ , and n denote the unit outward normal to ∂Ω. We are concerned with the Neumann boundary problems: −div(|x| α |∇u| p−2∇u) =|x| β u p(α,β)−1 − λ|xβ γ u p−1, u(x) > 0, x ∈ Ω, ∂u/∂n = 0 on ∂Ω, where 1 < p < N and α < 0, β < 0 such that $$ p(\alpha ,\beta ) \triangleq \frac{{p(N + \beta )}} {{N - p + \alpha }} $$ > p, γ > α−p. For various parameters α, β or γ, we establish certain existence results of the solutions in the case 0 ∈ Ω or 0 ∈ ∂Ω.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Sep 8, 2009
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