We consider weak non-negative solutions to the critical p-Laplace equationin the singular case 1 < p < 2. We prove that if p * 2 then all the solutions in D 1,p (R N ) are radial (and radially decreasing) about some point.
We consider weak solutions toWe exploit the Moser iteration technique to prove a Harnack comparison inequality for C 1 weak solutions. As a consequence we deduce a strong comparison principle.
In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the − p (•) operator and the Hardy-Leray potential. Assuming 0 ∈ Ω, we study the regularizing effect due to the addition of a first order nonlinear term, which provides the existence of solutions with a breaking of resonance. Once we have proved the existence of a solution, we study the qualitative properties of the solutions such as regularity, monotonicity and symmetry.
In this paper we obtain symmetry and monotonicity results for positive solutions to some p-Laplacian cooperative systems in bounded domains involving first-order terms and under zero Dirichlet boundary condition.
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