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Composition operators from Sobolev spaces into Lebesgue spaces

  • Aziz, Wadie [1]
    1. [1] Universidad de Los Andes

      Universidad de Los Andes

      Colombia

  • Localización: Divulgaciones matemáticas, ISSN-e 1315-2068, Vol. 20, Nº. 2, 2019 (Ejemplar dedicado a: Divulgaciones Matemáticas), págs. 45-62
  • Idioma: español
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • AbstractIn this paper, we shall obtain a compactness of weighted Sobolev embeddings and use it to get a composition operators from Sobolev spaces into Lebesgue spaces. Applying these re- sults we shall study the multiplicity for singular asymptotically linear p–Laplacian problems.ResumenEn este art´ıculo, obtenemos una compacidad de inmersiones de Sobolev ponderadas y lo usamos para tener operadores de composici´on del espacio de Sobolev en espacios de Lebes- gue. Aplicando estos resultados estudiaremos la multiplicidad para problemas p–laplacianos. 

  • Referencias bibliográficas
    • R. Adam and J. Fournier, Sobolev spaces. Academic Press, New York 2005.
    • Z. W. Birnbaum and W. Orlicz. U¨ber die verallgemeinerung des berriffes der zueinander konjugierten potenzen. Stu. Math., 30 (1968), 21–42.
    • A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973), 349–381.
    • A. Anane, Etude des valeurs propres et de la r´esonnance pour l’op´erateur p-laplacien. C. R. Ac. Sc. Paris, 305 (1987), 725–728.
    • J. Appell and P. Zabreiko, Nonlinear superposition operators. Cambridge University Press, 2008.
    • H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, 2011.
    • M. Cuesta. Eigenvalue problems for the p–laplacian with indefinite weights. Electronic Jour- nal of Differential Equations. 2001(33) (2001),...
    • G. Dinca, P. Jebelean and J. Mawhin. Variational and topological methods for Dirichlet problems with p–laplacian. Portugaliae Mathematica...
    • T. K. Donaldson and N. S. Trudinger. Orlicz-Sobolev spaces and imbedding theorems. J. Funct. Anal. 8 (1971), 52–75.
    • D. M. Duc and N. Q. Huy. Non-uniformly asymptotically linear p–Laplacian problems. Non- linear Analysis 92 (2013), 183–197.
    • D. M. Duc. Nonlinear singular elliptic equations. J. London Math. Soc. 40(2) (1989), 420– 440.
    • I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443–474. [13] D. G. De Figueiredo. Lectures on the Ekeland variational...
    • D. Gilbarg and N. S. Trudinger. Elliptic partial differential equations of second order, Springer, Berlin, 2001.
    • B. J. Jaye, V. G. Mazya and I. E. Verbitsky. Quasilinear elliptic equations and weighted Sobolev-Poincar´e inequalities with distributional...
    • M. A. Kranosel’skii. Topological methods in the theory of nonlinear integral equations. Macmillan, New York, 1964.
    • A. Kufner. Weighted Sobolev spaces. Wiley, New York, 1985.
    • A. Kufner, O. John and S. Fucik. Function spaces. Noordhoff, Leyden 1977. [19] S. Fucik and A. Kufner. Nonlinear Differential Equations. Vol....
    • M. Marcus and V. J. Mizel. Every superposition operator mapping one Sobolev space into another is continuous, J. Funct. Anal. 33 (1979), 217–229.
    • M. Marcus and V. J. Mizel. Complete characterization of functions which act, via superpo- sition, on Sobolev spaces. Transactions of AMS 251...
    • J. Matkwoski. Functional equation and Nemytskii operators. Funkc. Ekvac. 25 (1982) 127–132.
    • V. G. Mazja. Sobolev spaces, Springer, Berlin, 1985.
    • B. Opic and A. Kufner. Remark on compactness of imbeddings in weighted spaces. Math. Nachr. 133 (1987), 63–70.
    • T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. Series: De...
    • M. Struve. Variational methods. Springer, Berlin, 2008.
    • E. Zeidler. Nonlinear functional analysis and its applications III: Variational methods and optimization. Springer, Berl´ın, 1985.

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