On monotonicity of solutions of Dirichlet problem for some quasilinear elliptic equations in half-spaces - Salieva, Olga Alekseevna (Eurasian Mathematical Journal, 2015)
We prove the monotonicity of nonnegative bounded solutions to the Dirichlet problem for a quasilinear elliptic equation of the form \(-Δ_p u = f(u)g(x_n)\) with \(p ≥ 3\) in a half-space, where \(x_n\) is the normal coordinate of the argument. This assertion implies new nonexistence results for the case \(f(u) = u^q\) with the appropriate values of \(q\).