Special Session 66: Geometric insights in Partial Differential Equations: advances and challenges

Existence and decay for a Grushin problem in $\mathbb{R}^N$ with singular, convective, critical reaction
Paolo Malanchini
Universita` degli Studi di Milano - Bicocca
Italy
Co-Author(s):    Laura Baldelli, Paolo Malanchini and Simone Secchi
Abstract:
We establish an existence result for a problem set in the whole Euclidean space involving the Grushin operator and featuring a critical term perturbed by a singular, convective reaction. Our approach combines variational methods, truncation techniques, and concentration-compactness arguments, together with set-valued analysis and fixed point theory. Additionally, we prove the decay at infinity of solutions in the absence of the convective term. The result is new even in the case where more than one feature between singularity, convectivity and criticality is taken into account. The talk is based on a joint work with Laura Baldelli (Karlsruhe Institute of Technology) and Simone Secchi (Universit\`{a} degli Studi di Milano - Bicocca).