Accesso libero

A bifurcation result involving Sobolev trace embedding and the duality mapping of W1,p



[1] Adams, R. A.: Sobolev spaces, Academic Press, New York, 1975.Search in Google Scholar

[2] Anane, A.: Simplicité et isolation de la première valeur propre du p-laplacien avec poids, Comptes Rendus de lAcadémie des Sciences-Series I-Mathematics 305 16(1987), 725728.Search in Google Scholar

[3] Atkinson, C., Champion, C. R.: Some boundary problems for the equation ∇ · (|∇φ|Nφ) = 0, Q. J. Mech. Appl. Math. 37(1983), 401-419.10.1093/qjmam/37.3.401Search in Google Scholar

[4] Atkinson, C., Jones, C. W.: Similarity solutions in some nonlinear diffusion problems and in boundarylayer flow of a pseudo plastic fluid, Q. J. Mech. Appl. Math. 27(1974), 193-211.10.1093/qjmam/27.2.193Search in Google Scholar

[5] Babuska, I., Osborn, J.: Eigenvalue problems, in “Handbook of numerical analysis”, Vol. II, North- Holland, Amsterdam, (1991), 314-787.Search in Google Scholar

[6] Beurling, A., Livingston, A.: A theorem on duality mappings in Banach space, Ark. Mat. 4(1962), 405-411.10.1007/BF02591622Search in Google Scholar

[7] Binding, P. A., Huang, Y. X.: Bifurcation from eigencurves of the p-Laplacian, Diff. Int. Equations 8 no. 2 (1995), 415-418.Search in Google Scholar

[8] Browder, F. E.: On a theorem of Beurling and Livingston, Cand. J. Math. 17(1965), 367-372.10.4153/CJM-1965-037-2Search in Google Scholar

[9] Browder, F. E., Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. 9(1983), 1-39.10.1090/S0273-0979-1983-15153-4Search in Google Scholar

[10] Browder, F. E., Petryshyn, W. F.: Approximation methods and the generalized topological degree for nonlinear mapping in Banach spaces, J. Funct. Anal. 3(1969), 217-245.10.1016/0022-1236(69)90041-XSearch in Google Scholar

[11] Bronder, J. F., Rossi, J. D.: A nonlinear eigenvalue problem with indefinite weights related to Sobolev trace embedding, Publ. Mat. 46(2002), 221-235.10.5565/PUBLMAT_46102_12Search in Google Scholar

[12] Crîngnu, J.:Variational and topological methods for Neumann problems with p-Laplacian, Communications on Applied Nonlinear Analysis 11(2004), 1-38.Search in Google Scholar

[13] Ciorǎnascu, I.: Duality mapping in nonlinear functional analysis, Publishing House of Romanian Academy Bucharest, 1974. (in Romanian).Search in Google Scholar

[14] Del Pino, M. A., Manesevich, R. F.: Global bifurcation from the eigenvalues of the p-Laplacian, J. Diff. Equations 130(1996), 235-246.10.1006/jdeq.1996.0140Search in Google Scholar

[15] De Thélin,F.: Sur l’espace propre associé à la première valeur propre du pseudo-laplacien, Comptes Rendus Mathmatique. Académie des Sciences. Paris, Sér. I Math., 303(1986), 355-358.Search in Google Scholar

[16] Diaz, J. I., Nonlinear partial differential equations and free boundaries, Vol. I, Elliptic Equations, London, 1985.Search in Google Scholar

[17] Drábek, P., El khalil, A., Touzani A., A result on the bifurcation from the principal eigenvalue of the Ap-Laplacian, Abstract and Applied Analysis, vol. 2, Nos. 3-4 (1997), 185-195.10.1155/S108533759700033XSearch in Google Scholar

[18] Drábek, P., El khalil, A., Touzani A., A bifurcation Problem for the Principal Eigencurve of the p- Laplacian, Applicable Analysis, vol. 72, Nos. 3-4 (1999), 399-410.10.1080/00036819908840749Search in Google Scholar

[19] Drábek, P., Huang, Y. X., Bifurcation problems for the p-Laplacian inn, Trans-Amer, Math. Soc. 349(1997), 171-188.10.1090/S0002-9947-97-01788-1Search in Google Scholar

[20] Edmunds, D.E., Evans, W.D., Spectral Theory and Differential Operators, Clarendon Press, University Oxford Press, New York, 1987.Search in Google Scholar

[21] El khalil, A., Touzani A.:On the first eigencurve of the p-Laplacian, Partial Differential Equations, Lecture Notes in Pure and Applied Mathematics Series, Marcel Dekker, Inc. 229(2002), 195-205.Search in Google Scholar

[22] Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second order, Springer, Berlin, 1983.Search in Google Scholar

[23] Lindqvist, P.: On the equation div(|∇u|p−2u) + λ|u|p−2u = 0, Proc. Amer. Math. Soc. 109(1990), 157-164.Search in Google Scholar

[24] Pao, C. V.: Nonlinear parabolic and elliptic equations, Plenum Press, New York, London, 1992.10.1007/978-1-4615-3034-3Search in Google Scholar

[25] Pelissier, M. C.: Sur quelques problèmes non linéaires en glaciologie, Thèse, Publications Mathématiques d’Orsay, No. 110, 1975.Search in Google Scholar

[26] Philip, J. R.: N-diffusion, Aust. J. Phys. 14(1961), 1-13.10.1071/PH610001Search in Google Scholar

[27] Rabinowitz, P. H.: Some global results for nonlinear eigenvalue problem, J. Funct. Anal. 7(1971), 487-513.10.1016/0022-1236(71)90030-9Search in Google Scholar

[28] Skrypnik, I. V.: Nonlinear Elliptic Boundary Value Problem, Teubner, Leipzig, 1986.Search in Google Scholar