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Singular equations with variable exponents and concave-convex nonlinearities

  • Corresponding author: Leszek Gasiński

    Corresponding author: Leszek Gasiński 
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  • We consider a nonlinear anisotropic Dirichlet problem with a reaction that has the combined effects of three distinct nonlinearities: a parametric singular term, a parametric "concave" term (the parameter $ \lambda>0 $ is the same in both) and a nonparametric "convex" perturbation. So, the problem is a singular version of the well known "concave-convex" problem. We prove an existence and multiplicity result which is global in the parameter $ \lambda>0 $ (a bifurcation-type theorem). We also indicate some small improvements in the case of $ (p(z),q(z)) $ and $ p(z) $-equations.

    Mathematics Subject Classification: Primary: 35J20; Secondary: 35J60.


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