FAN Hai-Ning , LIU Xiao-Chun . EXISTENCE RESULTS FOR DEGENERATE ELLIPTIC EQUATIONS WITH CRITICAL CONE SOBOLEV EXPONENTS[J]. Acta mathematica scientia, Series B, 2014 , 34(6) : 1907 -1921 . DOI: 10.1016/S0252-9602(14)60134-X

[1] Ambrosetti A, Brezis H, Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J Funct Anal, 1994, 122: 519–543

[2] Chen H, Liu X, Wei Y. Existence theorem for a class of semilinear elliptic equations with critical cone Sobolev exponent. Ann Glob Anal Geom, 2011, 39: 27–43

[3] Chen H, Liu X, Wei Y. Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities. Cal Var Partial Differ, 2012, 43: 463–484

[4] Chen H, Liu X, Wei Y. Multiple solutions for semilinear totally characteristic equations with subcritical or critical cone sobolev exponents. J Differ Equ, 2012, 252: 4200–4228

[5] Chen H, Liu X, Wei Y. Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term. J Differ Equ, 2012, 252: 4289–4314

[6] Chen H, Wei Y, Zhou B. Existence of solutions for degenerate elliptic equations with singular potential on singular manifolds. Math Nachrichten, 2012, 285: 1370–1384

[7] Egorov Ju V, Schulze B -W. Pseudo-Differential Operators, Singularities, Applications. Operator Theory, Advances and Applications 93. Basel: Birkh¨auser Verlag, 1997

[8] Fan H, Liu X. Multiple positive solutions for degenerate elliptic equations with critical cone Sobolev exponents on singular manifolds. Elec J Diff Equ, 2013, 2013: 1–22

[9] Fan H. Existence theorems for a class of edge-degenerate elliptic equations on singular manifolds. Proceedings of the Edinburgh Mathematical Society, in press

[10] Garcia J, Peral I. Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term. Trans Amer Math Soc, 1991, 323: 941–957

[11] Kondrat’ev V A. Bundary value problems for elliptic equations in domains with conical points. Tr Mosk Mat Obs, 1967, 16: 209–292

[12] Liu X, Yuan M. Existence of nodal solution for semi-linear elliptic equations with critical Sobolev exponent on singular manifold. Acta Math Sci, 2013, 33B(2): 543–555

[13] Lions P L. The concentration-compactness principle in the calculus of variations, the locally comapct case. Ann Inst H Poincare Anal Nonlineaire, 1984, 1(Part 1): 109–145; 1984, 2(Part 2): 223–283

[14] Lions P L. The concentration-compactness principle in the calculus of variations: the limit case. Rev Mat Ibero Americana, 1985, 1(Part 1): 145–201; 1985, 2(Part 2): 45–121

[15] Mazzeo R. Elliptic theory of differential edge operators I. Comm Partial Differ Equ, 1991, 16: 1615–1664

[16] Melrose R B, Mendoza G A. Elliptic operators of totally characteristic type. PreprintMath Sci Res Institute, MSRI, 1983: 47–83

[17] Melrose R B, Piazza P. Analytic K-theory on manifolds with cornners. Adv Math, 1992, 92: 1–26

[18] Ouyang T, Shi J. Exact multiplicity of positive solutions for a class of semilinear problem II. J Differ Equ, 1999, 158: 94–151

[19] Schulze B -W. Boundary Value Problems and Singular Pseudo-Differential Operators. Chichester: John Wiley, 1998

[20] Schrohe E, Seiler J. Ellipticity and invertiblity in the cone algebra on L p-Sobolev spaces. Integral Equations Operator Theory, 2001, 41: 93–114

[21] Struwe M. Variational Methods, 2nd ed. Berlin, Heidelberg: Springer-Verlag, 1996

[22] Tang M. Exact multiplicity for semilinear elliptic Dirichlet problems involving concave and convex nonlinearities. Proc Royal Soc Edinburgh, 2003, 133A: 705–717

[23] Willem W. Minimax Theorems. Birkhauser, 1996