Singular Anisotropic Problems with Competition Phenomena

Abstract

Abstract We consider a Dirichlet problem driven by the anisotropic ( p ( z ), q ( z ))-Laplacian, with a parametric reaction exhibiting the combined effects of singular and concave-convex nonlinearities. The superlinear term may change sign. Using variational tools together with truncation and comparison techniques, we prove a global (for the parameter $$\lambda &gt;0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ) existence and multiplicity theorem (a bifurcation-type theorem).

Topics & Concepts