40 Mousomi Bhakta - Lane–Emden equations with Hardy potential and measure data

IISc-IISER Pune Twenty-20 Symposium 2021: https://sites.google.com/view/iisc-ii... Talk-40, Sep 18, 2021 Abstract: I will discuss the multiplicity of positive solutions to Lane–Emden equations and systems of equations with Hardy potential and measure data, namely equation of the form −∆u −μ u / δ^2 = u^p in Ω, u = ρν on ∂Ω, where δ(x) = dist(x, ∂Ω), μ and ρ are positive parameters and μ is strictly smaller than the best Hardy constant. ν is a positive Radon measure on ∂Ω with norm 1 and p ∈ (1, N_μ), with N_μ being a critical exponent depending on N and μ.