Existence and regularity for a p-Laplacian problem in ℝN with singular, convective, and critical reaction

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 C1,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.

Keywords

• mountain pass theorem
• concentration compactness
• set-valued analysis
• fixed point theory
• gradient estimates
• 35j92
• 35j20
• 35b08
• 35b45