AbstractThe aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators.
AbstractIn this article we prove the existence of at least two weak solutions for a Kirchhoff-type problem by using the minimum principle, the mountain pass theorem and variational methods in Orlicz–Sobolev spaces.
UDC 517.9
The paper deals with the existence and multiplicity of nontrivial weak solutions for the
𝓅
(
x
)
-Kirchhoff-type problem,
u
=
Δ
u
=
0
o
n
∂
Ω
.
By using variational approach and Krasnoselskii’s genus theory, we prove the existence and multiplicity of solutions for the
𝓅
(
x
)
-Kirchhoff-type equation.
Abstract
Recently, the existence of at least two weak solutions for a Kirchhoff–type problem has been studied in [M. Makvand Chaharlang and A. Razani,
Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition,
Georgian Math. J. 28 2021, 3, 429–438]. Here, the existence of infinitely many solutions for nonlocal Kirchhoff-type systems including Dirichlet boundary conditions in Orlicz–Sobolev spaces is studied by using variational methods and critical point theory.
AbstractIn this paper, we consider the existence of solutions of the following Kirchhoff-type problem: $$\begin{aligned} \textstyle\begin{cases} - (a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx )\Delta u+ V(x)u=f(x,u) , & \text{in }\mathbb{R}^{3}, \\ u\in H^{1}(\mathbb{R}^{3}),\end{cases}\displaystyle \end{aligned}$$
{
−
(
a
+
b
∫
R
3
|
∇
u
|
2
d
x
)
Δ
u
+
V
(
x
)
u
=
f
(
x
,
u
)
,
in
R
3
,
u
∈
H
1
(
R
3
)
,
where $a,b>0$
a
,
b
>
0
are constants, and the potential $V(x)$
V
(
x
)
is indefinite in sign. Under some suitable assumptions on f, the existence of solutions is obtained by Morse theory.
In this article, we study the existence of solutions for nonlocal
p
x
-biharmonic Kirchhoff-type problem with Navier boundary conditions. By different variational methods, we determine intervals of parameters for which this problem admits at least one nontrivial solution.
On
𝓅
(
x
)
-Kirchhoff-type equation involving
𝓅
(
x
)
-biharmonic operator via genus theor
