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

Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex... 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 $$\lambda >0$$ λ > 0 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

, Volume 20 (4) – Jan 13, 2016
35 pages

/lp/springer_journal/positive-solutions-for-nonlinear-nonhomogeneous-dirichlet-problems-vsK9C6n6pS
Publisher
Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0395-8
Publisher site
See Article on Publisher Site

### 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 $$\lambda >0$$ λ > 0 .

### Journal

PositivitySpringer Journals

Published: Jan 13, 2016

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