On the Gibbons’ conjecture for equations involving the p-Laplacian

Abstract

AbstractIn this paper we prove the validity of Gibbons’ conjecture for the quasilinear elliptic equation $$ -\Delta _p u = f(u) $$ - Δ p u = f ( u ) on $$\mathbb {R}^N.$$ R N . The result holds true for $$(2N+2)/(N+2)< p < 2$$ ( 2 N + 2 ) / ( N + 2 ) < p < 2 and for a very general class of nonlinearity f.