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Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory

  • Massimo Grossi
  • Angela Pistoia
  • Juncheng Wei
Original article

Abstract.

We study a perturbed semilinear problem with Neumann boundary condition

\(\)

where \(\Omega\) is a bounded smooth domain of \({mathbb{R}}^N\), \(N\ge2\), \(\varepsilon>0\), \(1 < p < {{N+2}\over{N-2}}\) if \(N\ge3\) or \(p>1\) if \(N=2\) and \(\nu\) is the unit outward normal at the boundary of \(\Omega\). We show that for any fixed positive integer K any “suitable” critical point \((x_0^1,\dots,x_0^K)\) of the function

\(\)

generates a family of multiple interior spike solutions, whose local maximum points \(x_\varepsilon^1,\dots,x_\varepsilon^K\) tend to \(x_0^1,\dots,x_0^K\) as \(\varepsilon\) tends to zero.

Mathematics Subject Classification (1991): 35J40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Massimo Grossi
    • 1
  • Angela Pistoia
    • 2
  • Juncheng Wei
    • 3
  1. 1.Dipartimento di Matematica, Università di Roma “La Sapienza”, 00185 Roma, Italy (e-mail: grossi@mat.uniromA1.it)IT
  2. 2.Dipartimento di metodi e modelli matematici, Università di Roma “La Sapienza”, 00185 Roma, Italy (e-mail: pistoia@dmmm.uniromA1.it)IT
  3. 3.Department of Mathematics, The Chinese University of Honk Kong, Shatin (e-mail: wei@math.cuhk.edu.hk)HK

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