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A Dirichlet problem with singular and supercritical nonlinearities. (English) Zbl 1250.35112
The author proves the existence of positive solutions in W 0 1,2 (Ω)L (Ω) for a Dirichlet problem with singular and supercritical nonlinearities.
Reviewer: Jiaqi Mo (Wuhu)
MSC:
35J66Nonlinear boundary value problems for nonlinear elliptic equations
35B09Positive solutions of PDE
References:
[1]Boccardo, L.; Escobedo, M.; Peral, I.: A Dirichlet problem involving critical exponent, Nonlinear anal. TMA 24, 1639-1648 (1995) · Zbl 0828.35042 · doi:10.1016/0362-546X(94)E0054-K
[2]Ambrosetti, A.; Brezis, H.; Cerami, G.: Combined effects of concave and convex nonlinearities in some elliptic problems, J. funct. Anal. 122, 519-543 (1994) · Zbl 0805.35028 · doi:10.1006/jfan.1994.1078
[3]Boccardo, L.; Orsina, L.: Semilinear elliptic equations with singular nonlinearities, Calc. var. Partial differential equations 37, 363-380 (2010) · Zbl 1187.35081 · doi:10.1007/s00526-009-0266-x
[4]Coclite, M. M.; Palmieri, G.: On a singular nonlinear Dirichlet problem, Comm. partial differential equations 14, 1315-1327 (1989) · Zbl 0692.35047 · doi:10.1080/03605308908820656
[5]Stuart, C. A.: Existence and approximation of solutions of nonlinear elliptic equations, Math. Z. 147, 53-63 (1976) · Zbl 0324.35037 · doi:10.1007/BF01214274
[6]Canino, A.; Degiovanni, M.: A variational approach to a class of singular semilinear elliptic equations, J. convex anal. 11, 147-162 (2004) · Zbl 1073.35092 · doi:http://www.heldermann.de/JCA/JCA11/jca11010.htm
[7]Hirano, N.; Saccon, C.; Shioji, N.: Brezis–Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem, J. differential equations 245, 1997-2037 (2008) · Zbl 1158.35044 · doi:10.1016/j.jde.2008.06.020