On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half

Abstract

Abstract. We study the existence of positive continuous solutions of the nonlinear polyharmonic system (−∆) m u + λqg(v) = 0, (−∆) m v + µpf (u) = 0 in the half space R n + := {x = (x1, . . . , xn) ∈ R n : xn > 0}, where m ≥ 1 and n > 2m. The nonlinear term is required to satisfy some conditions related to the Kato class K ∞ m,n (R n + ). Our arguments are based on potential theory tools associated to (−∆) m and properties of functions belonging to K ∞ m,n (R n + ).

An Existence Result for a Class of Coupled Polyharmonic Systems

“…The investigation of coupled higher-order systems involving the polyharmonic operator (−∆) m , m ≥ 2, has recently appeared in the literature [15][16][17].…”