Existence of Solutions for Some p(x)-polyharmonic Elliptic Kirchhoff Equations

摘要

In this paper, we study the existence of solution for some p (x ) -polyharmonic Kirchhoff equations. The latter is allowed to vanish at the origin (degenerate case). Firstly, we study the existence of solutions of approximate equations. Secondly, we prove the existence of the solutions of the original equation. The main tool is the Schauder’s Theorem.