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Generic Fredholm alternative-type results for the one dimensional p-Laplacian

  • Pavel Drábek
  • Petr Girg
  • Raul Manásevich

Abstract.

In this paper we give a generic necessary and sufficient condition for the solvability of¶\( (|u'|^{p-2} u')' + (p-1) |u|^{p-2} u = h \;in\; (0, \pi_p),\quad u(0) = u (\pi_p)= 0. \)

Key words: p-Laplacian, Fredholm alternative, Leray-Schauder degree, upper and lower solutions. 

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Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • Pavel Drábek
    • 1
  • Petr Girg
    • 2
  • Raul Manásevich
    • 3
  1. 1.Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Plzeň, Czech Republic, e-mail: pdrabek@kma.zcu.czCZ
  2. 2.Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Plzeň, Czech Republic, e-mail: pgirg@kma.zcu.czCZ
  3. 3.Departamento de Ingenierí a Matemática, FCFM, Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile, e-mail: manasevi@dim.uchile.clCL

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