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Set-Valued and Variational Analysis

, Volume 19, Issue 1, pp 1–21 | Cite as

Boundary Value Problems for Highly Nonlinear Inclusions Governed by Non-surjective Φ-Laplacians

  • Laura Ferracuti
  • Cristina MarcelliEmail author
  • Francesca Papalini
Article

Abstract

Combining fixed point theorems with the method of lower and upper solutions, we get the existence of solutions to the following nonlinear differential inclusion:
$$ (D(x(t))\Phi(x'(t)))' \in G(t,x(t),x'(t)) \ \ \mbox{a.e. } t\in I=[0,T], $$
satisfying various nonlinear boundary conditions, covering Dirichlet, Neumann and periodic problems. Here Φ is a non-surjective homeomorphism and D is a generic positive continuous function.

Keywords

Differential inclusions Φ-Laplacian Nonlinear boundary conditions Lower and upper solutions Fixed point techniques Nonlinear differential operators 

Mathematics Subject Classifications (2000)

Primary 34A60; Secondary 34L30 34B15 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Laura Ferracuti
    • 1
  • Cristina Marcelli
    • 1
    Email author
  • Francesca Papalini
    • 1
  1. 1.Department of Mathematical SciencesPolytechnic University of MarcheAnconaItaly

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