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Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus

  • Francesca Gladiali
  • Massimo Grossi
  • Filomena Pacella
  • P. N. Srikanth
Article

Abstract

In this paper we consider the problem
$$\left\{ \begin{array}{ll} -\Delta u=u^p+\lambda u & \quad\hbox{ in }A,\\ u > 0&\quad \hbox{ in }A,\\ u=0 &\quad \hbox{ on }\partial A, \end{array}\right. $$
where A is an annulus of \({\mathbb{R}^N,N\ge2}\) and p > 1. We prove bifurcation of nonradial solutions from the radial solution in correspondence of a sequence of exponents {p k } and for expanding annuli.

Mathematics Subject Classification (2000)

35J61 35B32 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Francesca Gladiali
    • 1
  • Massimo Grossi
    • 2
  • Filomena Pacella
    • 2
  • P. N. Srikanth
    • 3
  1. 1.Struttura dipartimentale di Matematica e FisicaUniversità di SassariSassariItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma “La Sapienza”RomeItaly
  3. 3.TIFR Centre for Applicable MathematicsBangaloreIndia

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