TITLE:
Existence of Solutions for (p1(x),p2(x)) -Triharmonic Problem with Navier Boundary Conditions
AUTHORS:
Zenghui Li, Qing Miao
KEYWORDS:
Variable Exponent Space, -Triharmonic Operator, Navier Boundary Condition, Mountain Pass Theorem, Fountain Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.2,
February
13,
2026
ABSTRACT: In this paper, we use the Mountain Pass theorem and the Fountain theorem to study the existence of solutions for the following
(
p
1
(
x
),
p
2
(
x
)
)
-triharmonic equations:
{
−
Δ
p
1
(
x
)
3
u−
Δ
p
2
(
x
)
3
u=f(
x,u
),
in Ω ,
u=Δu=
Δ
2
u=0,
on ∂Ω ,
. where the nonlinear term satisfying growth conditions weaker than Ambrosetti-Rabinowitz condition. We establish the existence of weak solutions using critical point theory and variational methods.