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Positivity

, Volume 20, Issue 4, pp 945–979 | Cite as

Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities

  • Nikolaos S. Papageorgiou
  • Patrick Winkert
Article

Abstract

We consider a nonlinear parametric Dirichlet equation driven by a nonhomogeneous differential operator involving a reaction exhibiting the competing effects of concave and convex terms. Using variational methods combined with truncation and comparison techniques we prove a bifurcation near zero theorem describing the dependence of the positive solutions on the parameter \(\lambda >0\).

Keywords

Nonhomogeneous differential operator Nonlinear regularity theory Nonlinear maximum principle Bifurcation of positive solutions Strong comparison Concave and convex nonlinearities 

Mathematics Subject Classification

35J66 35J70 35J92 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Institut für Mathematik, Technische Universität BerlinBerlinGermany

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