Infinitely many solutions for a p(x)-triharmonic equation with Navier boundary conditions

In this work, we will study the existence of an infinity of solutions of a Navier problem governed by the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>p</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {p(x)} -triharmonic operator using the theory of Ljusternick–Shrilemann and the theory of the variable exponent Sobolev spaces.