Artículo

Del Pezzo, L.M.; Quaas, A."Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian" (2017) Journal of Fixed Point Theory and Applications. 19(1):939-958
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Abstract:

In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional p-Laplacian. The first result is an existence in a non-resonant range more specific between the first and second eigenvalue of the fractional p-Laplacian. The second result is the anti-maximum principle for the fractional p-Laplacian. © 2017, Springer International Publishing.

Registro:

Documento: Artículo
Título:Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian
Autor:Del Pezzo, L.M.; Quaas, A.
Filiación:CONICET and Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Departamento de Matemática, Universidad Técnica Federico Santa María Casilla V-110, Avda. España, Valparaiso, 1680, Chile
Palabras clave:anti-maximum principle; existence results; Fractional p-Laplacian; non-resonant
Año:2017
Volumen:19
Número:1
Página de inicio:939
Página de fin:958
DOI: http://dx.doi.org/10.1007/s11784-017-0405-5
Handle:http://hdl.handle.net/20.500.12110/paper_16617738_v19_n1_p939_DelPezzo
Título revista:Journal of Fixed Point Theory and Applications
Título revista abreviado:J. Fixed Point Theory Appl.
ISSN:16617738
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16617738_v19_n1_p939_DelPezzo

Referencias:

  • Adams, R.A., (1975) Sobolev Spaces, Pure and Applied Mathematics, , 65, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York
  • Amghibech, S., On the discrete version of Picone’s identity (2008) Discrete Appl. Math., 156 (1), pp. 1-10
  • Anane, A., Simplicité et isolation de la première valeur propre du p -laplacien avec poids (1987) C. R. Acad. Sci. Paris Sér. I Math., 305 (16), pp. 725-728
  • Anane, A., Gossez, J., Strongly nonlinear elliptic problems near resonance: a variational approach (1990) Commun. Partial Differ. Equ., 15 (8), pp. 1141-1159
  • Anane, A., Tsouli, N., On a nonresonance condition between the first and the second eigenvalues for the p -Laplacian (2001) Int. J. Math. Math. Sci., 26 (10), pp. 625-634
  • Anane, A., Tsouli, N., On a nonresonance condition between the first and the second eigenvalue for the p -Laplacian (2004) Math. Rech. Appl., 6, pp. 101-114
  • Arcoya, D., Colorado, E., Leonori, T., Asymptotically linear problems and antimaximum principle for the square root of the Laplacian (2012) Adv. Nonlinear Stud., 12 (4), pp. 683-701
  • Arcoya, D., Gámez, J.L., Bifurcation theory and related problems: anti-maximum principle and resonance (2001) Commun. Partial Differ. Equ., 26 (9-10), pp. 1879-1911
  • Arcoya, D., Orsina, L., Landesman-Lazer conditions and quasilinear elliptic equations (1997) Nonlinear Anal., 28 (10), pp. 1623-1632
  • Arias, M., Campos, J., Gossez, J.-P., On the antimaximum principle and the Fučik spectrum for the Neumann p -Laplacian (2000) Differ. Integral Equ., 13 (1-3), pp. 217-226
  • Armstrong, S.N., Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations (2009) J. Differ. Equ., 246 (7), pp. 2958-2987
  • Birindelli, I., Hopf’s lemma and anti-maximum principle in general domains (1995) J. Differ. Equ., 119 (2), pp. 450-472
  • Boccardo, L., Drábek, P., Giachetti, D., Kučera, M., Generalization of Fredholm alternative for nonlinear differential operators (1986) Nonlinear Anal., 10, pp. 1083-1103
  • Bourgain, J., Brezis, H., Mironescu, P., Another look at sobolev spaces (2001) Menaldi, J.L., Rofman, E., Sulem, A. (Eds.) Optimal Control and Partial Differential Equations, A Volume in Honour of A. Bensoussan’s 60th Birthday, pp. 439–455. IOS Press
  • Brasco, L., Franzina, G., Convexity properties of Dirichlet integrals and Picone-type inequalities (2014) Kodai Math. J., 37 (3), pp. 769-799
  • Brasco, L., Parini, E., The second eigenvalue of the fractional p -Laplacian (2016) Adv. Calc. Var., 9 (4), pp. 323-355
  • Brasco, L., Parini, E., Squassina, M., Stability of variational eigenvalues for the fractional p -Laplacian (2016) Discrete Contin. Dyn. Syst., 36 (4), pp. 1813-1845
  • Clément, P., Peletier, L.A., An anti-maximum principle for second-order elliptic operators (1979) J. Differ. Equ., 34 (2), pp. 218-229
  • Cuesta, M., de Figueiredo, D., Gossez, J.-P., The beginning of the Fučik spectrum for the p -Laplacian (1999) J. Differ. Equ., 159 (1), pp. 212-238
  • Del Pezzo, L.M., Fernández Bonder, J., (1601) López Ros, L.: An optimization problem for the first eigenvalue of the p-fractional Laplacian. arXiv, p. 03019. , arXiv:1601.03019
  • Del Pezzo, L.M., Quaas, A., Global bifurcation for fractional p -Laplacian and application (2016) Z. Anal. Anwend., 35 (4), pp. 411-447
  • A Hopf’s lemma and a strong minimum principle for the fractional p -Laplacian, , Del Pezzo, L.M., Quaas, A.:
  • del Pino, M., Drábek, P., Manásevich, R., The Fredholm alternative at the first eigenvalue for the one-dimensional p -Laplacian (1999) J. Differ. Equ., 151 (2), pp. 386-419
  • Deimling, K., (1985) Nonlinear Functional Analysis, , Springer, Berlin
  • Demengel, F., Demengel, G., (2007) Functional spaces for the theory of elliptic partial differential equations. Universitext, Springer, London (2012), , Translated from the, French original by Reinie Erné
  • Di Nezza, E., Palatucci, G., Valdinoci, E., Hitchhiker’s guide to the fractional Sobolev spaces (2012) Bull. Sci. Math., 136 (5), pp. 521-573
  • Dolph, C.L., Nonlinear integral equations of the Hammerstein type (1949) Trans. Am. Math. Soc., 66, pp. 289-307
  • Drábek, P., The p -Laplacian–Mascot of nonlinear analysis (2007) Acta Math. Univ. Comenian. (N.S.), 76 (1), pp. 85-98
  • Drábek, P., Girg, P., Takáč, P., Ulm, M., The Fredholm alternative for the p -Laplacian: bifurcation from infinity, existence and multiplicity (2004) Indiana Univ. Math. J., 53 (2), pp. 433-482
  • Drábek, P., Girg, P., Manásevich, R., Generic Fredholm alternative-type results for the one dimensional p -Laplacian (2001) NoDEA Nonlinear Differ. Equ. Appl., 8 (3), pp. 285-298
  • Drábek, P., Takáč, P., A counterexample to the Fredholm alternative for the p -Laplacian (1999) Proc. Am. Math. Soc., 127 (4), pp. 1079-1087
  • Fleckinger, J., Gossez, J.-P., Takáč, P., François de Thélin, existence, nonexistence et principe de l’antimaximum pour le p -Laplacien (1995) C. R. Acad. Sci. Paris Sér. I Math., 321 (6), pp. 731-734
  • Franzina, G., Palatucci, G., Fractional p -eigenvalues (2014) Riv. Math. Univ. Parma (N.S.), 5 (2), pp. 373-386
  • García-Melián, J., Rossi, J.D., Maximum and antimaximum principles for some nonlocal diffusion operators (2009) Nonlinear Anal., 71 (12), pp. 6116-6121
  • Godoy, T., Gossez, J.-P., Paczka, S., On the antimaximum principle for the p -Laplacian with indefinite weight (2002) Nonlinear Anal., 51 (3), pp. 449-467
  • Sur le principe de l’antimaximum (1994) Cahiers Centre Études Rech. Opér, , Gossez, J.-P.. 36, 183–187 (Hommage à Simone Huyberechts)
  • Greco, A., Servadei, R., Hopf’s lemma and constrained radial symmetry for the fractional Laplacian. (English summary) (2016) Math. Res. Lett., 23 (3), pp. 863-885
  • Grisvard, P., (1985) Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, , 24, Pitman (Advanced Publishing Program), Boston
  • Global Hölder regularity for the fractional p -Laplacian (2014) Revista Matemática Iberoamericana, , Iannizzotto, A., Mosconi, S., Squassina, M.(To appear)
  • Lindgren, E., Lindqvist, P., Fractional eigenvalues (2014) Calc. Var. Partial Differ. Equ., 49 (1-2), pp. 795-826
  • Lindqvist, P., On the equation div(|∇u|p-2∇u)+λ|u|p-2u=0 (1990) Proc. Am. Math. Soc., 109 (1), pp. 157-164
  • Lindqvist, P., Addendum: “On the equation div (| ∇ u| p - 2∇ u) + λ| u| p - 2u= 0 (1992) Proc. Am. Math. Soc., 116 (2), pp. 583-584
  • Manásevich, R., Takáč, P., On the Fredholm alternative for the p -Laplacian in one dimension (2002) Proc. Lond. Math. Soc. (3), 84 (2), pp. 324-342
  • Parini, E., Continuity of the variational eigenvalues of the p -Laplacian with respect to p (2011) Bull. Aust. Math. Soc., 83 (3), pp. 376-381
  • Ros-Oton, X., Serra, J., The Dirichlet problem for the fractional Laplacian: regularity up to the boundary (2014) J. Math. Pures et Appl. (9), 101 (3), pp. 275-302
  • Servadei, R., Valdinoci, E., Variational methods for non-local operators of elliptic type (2013) Discrete Contin. Dyn. Syst., 33 (5), pp. 2105-2137
  • Servadei, R., Valdinoci, E., A Brezis–Nirenberg result for non-local critical equations in low dimension (2013) Commun. Pure Appl. Anal., 12 (6), pp. 2445-2464
  • Servadei, R., Valdinoci, E., On the spectrum of two different fractional operators (2014) Proc. R. Soc. Edinb. Sect. A, 144 (4), pp. 831-855
  • Servadei, R., Valdinoci, E., Weak and viscosity solutions of the fractional Laplace equation (2014) Publ. Mat., 58 (1), pp. 133-154
  • Takáč, P., On the Fredholm alternative for the p -Laplacian at the first eigenvalue (2002) Indiana Univ. Math. J., 51 (1), pp. 187-237
  • Takáč, P., A variational approach to the Fredholm alternative for the p -Laplacian near the first eigenvalue (2006) J. Dyn. Differ. Equ., 18 (3), pp. 693-765

Citas:

---------- APA ----------
Del Pezzo, L.M. & Quaas, A. (2017) . Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian. Journal of Fixed Point Theory and Applications, 19(1), 939-958.
http://dx.doi.org/10.1007/s11784-017-0405-5
---------- CHICAGO ----------
Del Pezzo, L.M., Quaas, A. "Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian" . Journal of Fixed Point Theory and Applications 19, no. 1 (2017) : 939-958.
http://dx.doi.org/10.1007/s11784-017-0405-5
---------- MLA ----------
Del Pezzo, L.M., Quaas, A. "Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian" . Journal of Fixed Point Theory and Applications, vol. 19, no. 1, 2017, pp. 939-958.
http://dx.doi.org/10.1007/s11784-017-0405-5
---------- VANCOUVER ----------
Del Pezzo, L.M., Quaas, A. Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian. J. Fixed Point Theory Appl. 2017;19(1):939-958.
http://dx.doi.org/10.1007/s11784-017-0405-5