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2015 | 13 | 1 |
Tytuł artykułu

Semilinear problems for the fractional laplacian with a singular nonlinearity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to study the solvability of the problem [...] where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 < s < 1, γ > 0, λ > 0, p > 1 and f is a nonnegative function. We distinguish two cases: – For M = 0, we prove the existence of a solution for every γ > 0 and λ > 0. A1 – For M = 1, we consider f ≡ 1 and we find a threshold ʌ such that there exists a solution for every 0 < λ < ʌ ƒ, and there does not for λ > ʌ ƒ
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-12-16
zaakceptowano
2015-05-28
online
2015-06-11
Twórcy
  • Departamento de Matemáticas, Universidad Autonoma de Madrid, Spain
autor
  • Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza, Università di Roma, Italy
  • Departamento de Matemáticas, Universidad Autonoma de Madrid, Spain
autor
  • Departamento de Matemáticas, Universidad Autonoma de Madrid, Spain
Bibliografia
  • [1] Ambrosetti A., Brezis H., Cerami G., Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct.Anal., 1994, 122(2), 519-543
  • [2] Ambrosetti A., Rabinowitz P. H., Dual variational methods in critical point theory and applications, J. Funct. Anal., 1973, 14,349-381[Crossref]
  • [3] Arcoya D., Boccardo L., Multiplicity of solutions for a Dirichlet problem with a singular and a supercritical nonlinearities, DifferentialIntegral Equations, 2013, 26, 119-128
  • [4] Arcoya D., Moreno-Merida L., Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity, Nonlinear Anal.,2014, 95, 281-291
  • [5] Barrios B., Colorado E., Servadei R., Soria F., A critical fractional equation with concave-convex nonlinearities, Ann. Inst.H. Poincaré Anal. Non Linéaire (in press), DOI: 10.1016/j.anihpc.2014.04.003[Crossref]
  • [6] Barrios B., Medina M., Peral I., Some remarks on the solvability of non local elliptic problems with the Hardy potential. Commun.Contemp. Math., 2014, 16, 4[Crossref][WoS]
  • [7] Boccardo L., Orsina L., Semilinear elliptic equations with singular nolinearities, Calc. Var. Partial Differential Equations, 2010,37(3-4), 363-380
  • [8] Boccardo L., A Dirichlet problem with singular and supercritical nonlinearities, Nonlinear Anal., 2012, 75, 4436-4440
  • [9] Boccardo L., Escobedo M., Peral I., A Dirichlet problem involving critical exponent, Nonlinear Anal., 1995, 24, 1639-1848
  • [10] Brezis H. , Kamin S., Sublinear elliptic equations in Rn, Manuscripta Math., 1992, 74, 87–106
  • [11] Brezis H., Nirenberg L., H1 versus C1 local minimizers, C. R. Acad. Sci. Paris t., 1993, 317, 465-472
  • [12] Canino A., Degiovanni M., A variational approach to a class of singular semilinear elliptic equations, Journal of Convex Analysis,2004, 11(1), 147-162
  • [13] Crandall M. G., Rabinowitz P. H., Tartar L., On a Dirichlet problem with a singular nonlinearity, Comm. Partial DifferentialEquations, 1977, 2, 193-222
  • [14] Coclite M. M., Palmieri G., On a singular nonlinear Dirichlet problem, Comm. Partial Differential Equations, 1989, 14(10),1315-1327
  • [15] Dávila J., A strong maximum principle for the Laplace equation with mixed boundary condition, J. Funct. Anal., 2001, 183,231-244
  • [16] Di Nezza E., Palatucci G., Valdinoci E., Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math., 2012, 136(5),521-573[WoS]
  • [17] García Azorero J. P., Peral I., Multiplicity of solutions for elliptic problems with critical exponents or with a non-symmetric term,Transactions American Mathematical Society, 1991, 323(2), 877-895
  • [18] García Azorero J. P., Manfredi J. J., Peral I., Sobolev versus Hölder local minimizers and global multiplicity for some quasilinearelliptic equations, Commun. Contemp. Math., 2000, 2(3), 385-404[Crossref]
  • [19] Ghergu M., Radulescu V., Singular elliptic problems with convection term in anisotropic media, Mathematical analysis andapplications, 2006, 74-89, AIP Conf. Proc., 835, Amer. Inst. Phys., Melville, NY
  • [20] Ghoussoub N., Preiss D., A general mountain pass principle for locating and classifying critical points. Ann. Inst. H. PoincaréAnal. Non Linéaire, 1989, 6(5), 321-330
  • [21] Hirano N., Saccon C., Shioji N., Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem,J. Differential Equations, 2008, 245, 1997-2037
  • [22] Greco A., Servadei R., Hopf’s lemma and constrained radial symmetry for the fractional laplacian, preprint
  • [23] Lair A. V., Shaker A. W., Classical and Weak Solutions of a Singular Semilinear Elliptic Problem, Journal of Mathematical Analysisand Applications, 1997, 211, 371-385
  • [24] Landkof N., Foundations of modern potential theory, Die Grundlehren der mathematischen Wissenschaften, Band 180. Springer-Verlag, New York-Heidelberg, 1972
  • [25] Lazer A. C., McKenna P. J., On a Singular Nonlinear Elliptic Boundary-Value Problem, Proceedings of the American MathematicalSociety, 1991, 111(3), 721-730
  • [26] Lazer A. C., McKenna P. J., On Singular Boundary Value Problems for the Monge-Ampère Operator, Journal of MathematicalAnalysis and Applications, 1996, 197, 341-362
  • [27] Leonori T., Peral I., Primo A., Soria F., Basic estimates for solution of elliptic and parabolic equations for a class of nonlocaloperators, preprint
  • [28] Ros-Oton X., Serra J., The Dirichlet problem for the fractional laplacian: regularity up to the boundary, J. Math. Pures Appl. (9),2014, 101(3), 275-302
  • [29] Servadei R., Valdinoci E., Mountain Pass solutions for non-local elliptic operators, J. Math. Anal. Appl., 2012, 389(2), 887-898[WoS]
  • [30] Servadei R., Valdinoci E., Variational methods for non-local operators of elliptic type, Discrete Contin. Dyn. Syst., 2013, 33(5),2105-2137[WoS]
  • [31] Silvestre L., Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 2007,60(1), 67-112[WoS]
  • [32] Stampacchia G., Le probléme de Dirichlet pour les équations elliptiques du second ordre á coefficients discontinus, Ann. Inst.Fourier (Grenoble), 1965, 15, fasc. 1, 189-258[Crossref]
  • [33] Stein E. M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30 PrincetonUniversity Press, Princeton, N.J. 1970
  • [34] Stuart C. A., Self-trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rational Mech. Anal.,1991, 113, 65-96[Crossref]
  • [35] Zhang Z., Boundary behavior of solutions to some singular elliptic boundary value problems. Nonlinear Anal., 2008, 69(7),2293-2302
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0038
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