Abstract We prove an existence result for a p-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi’s technique, a priori gradient estimates, and nonlinear regularity theory are employed to obtain local C 1 , α {C}^{1,\alpha } regularity of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian.
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