Multiple Solutions for a Variable‐Order p(x,·)‐Kirchhoff‐Type Problem With Weight

ABSTRACT In this study, we establish the existence of three weak solutions for a Kirchhoff‐type problem with weight that involves the variable‐order ‐Laplacian operator. We introduce a suitable functional framework for addressing such problems and establish a fundamental continuous and compact embedding theorem of this framework. Using Ricceri's three critical point approach, we prove the existence of weak solutions in the context of weighted variable‐order Sobolev spaces with variable exponents.