Existence results for some polyharmonic problems in the half-space

Abstract

We study the existence of positive solutions of the m-polyharmonic nonlinear elliptic equation (−Δ) m u+ f (·, u) = 0 in the half-space R n + := {x = (x 1 , . . . , x n ) ∈ R n : x n > 0}, n 2 and m 1. Our purpose is to give two existence results for the above equation subject to some boundary conditions, where the nonlinear term f (x, t) satisfies some appropriate conditions related to a certain Kato class of functions K ∞ m,n (R n + ).

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

“…The class K ∞ m,n was fully developed and exploited to study the existence of positive continuous solutions for some polyharmonic nonlinear elliptic problems (see [4,5]). …”