Parametric singular double phase Dirichlet problems
Yunru Bai, Nikolaos S. Papageorgiou, Shengda Zeng
Abstract
Abstract We consider a parametric (with two parameters <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>λ</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> \mu ,\lambda \gt 0 ) Dirichlet problem driven by the double phase differential operator and a reaction which has the competing effect of a singular term and of a superlinear perturbation. We prove a bifurcation-type result in the parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> \lambda \gt 0 , when the other parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> \mu \gt 0 is large.