Global Multiplicity of Positive Solutions for a Sublinear Elliptic Equation in Rn

We establish global multiplicity of positive solutions (existence and nonexistence theory) for the following problem {Δu+λh(x)f(u)=0inRN,u>0inRN,u∈D1,2(RN), where N≥3, λ>0 is a parameter, 0≤h∈L∞(RN) and f is a sublinear nonlinearity at ∞. In order to obtain our results we use a combination of the sub- super solution method and variational techniques. For instance, we need to implement a relevant result of type D1,2(RN) versus X local minimizer for some appropriate space X. © 2024 Elsevier Inc.