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A Semilinear Elliptic Equation on RN with Unbounded Coefficients

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Variational and Topological Methods in the Study of Nonlinear Phenomena

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 49))

Abstract

We study the existence of localized solutions of the semilinear elliptic equation

$$- \Delta u + a(x)u = f(x,u)$$

on ℝN. Many papers deal with the case when a is “large” at infinity and f is subcritical: for some c > 0 and \(p < \tfrac{{2N}}{{(N - 2)}}\),

$$|f(x,u)| \leqslant c(1 + |u{|^{p - 1}}),$$

see, e.g., [1], [2], [4], [5].

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References

  1. T. Bartsch and Z.-W. Wang, Existence and multiplicity results for some superlinear elliptic problems on >18N, Comm. Partial Differential Equations 20 (1995), 1725–1741.

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Author information

Authors and Affiliations

  1. Département de Mathématiques Université Catholique, Louvain-La-Neuve, Belgium

    P. Sintzoff & M. Willem

Authors
  1. P. Sintzoff
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  2. M. Willem
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica Applicata, Universita di Pisa, Pisa, 56126, Italy

    V. Benci  & A. M. Micheletti  & 

  2. Dipartimento di Matematica ed Applicazioni, Universita di Palermo, Palermo, 90123, Italy

    G. Cerami

  3. Dipartimento di Matematica e Fisica, Universita Cattolica del Sacro Cuore, Brescia, 25121, Italy

    M. Degiovanni

  4. Dipartimento Interuniversitario di Matematica, Universita di Bari, Bari, 70125, Italy

    D. Fortunato

  5. Dipartimento di Matematica e Fisica, Universita di Camerino, Camerino, 62032, Italy

    F. Giannoni

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© 2002 Springer Science+Business Media New York

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Sintzoff, P., Willem, M. (2002). A Semilinear Elliptic Equation on RN with Unbounded Coefficients. In: Benci, V., Cerami, G., Degiovanni, M., Fortunato, D., Giannoni, F., Micheletti, A.M. (eds) Variational and Topological Methods in the Study of Nonlinear Phenomena. Progress in Nonlinear Differential Equations and Their Applications, vol 49. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0081-9_8

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  • DOI: https://doi.org/10.1007/978-1-4612-0081-9_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6604-4

  • Online ISBN: 978-1-4612-0081-9

  • eBook Packages: Springer Book Archive

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