scholarly journals Existence of solutions for a p-Laplacian Kirchhoff type problem with nonlinear term of superlinear and subcritical growth

2020 ◽  
Vol 65 (4) ◽  
pp. 521-542
Author(s):  
Melzi Imane ◽  
Moussaoui Toufik
Keyword(s):  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Type Problem ◽  
Subcritical Growth ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Problem

"This paper is concerned by the study of the existence of nonnegative and nonpositive solutions for a nonlocal quasilinear Kirchhoff problem by using the Mountain Pass lemma technique."

scholarly journals On a p x -Biharmonic Kirchhoff Problem with Navier Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hafid Lebrimchi ◽  
Mohamed Talbi ◽  
Mohammed Massar ◽  
Najib Tsouli
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Nontrivial Solution ◽  
Existence Of Solutions ◽  
Type Problem ◽  
Navier Boundary Conditions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Problem

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.

Multi-bump solutions for a Kirchhoff-type problem

2016 ◽  
Vol 5 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Claudianor O. Alves ◽  
Giovany M. Figueiredo
Keyword(s):  
Existence Of Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Problem

AbstractIn this paper, we study the existence of solutions for the Kirchhoff problem

scholarly journals Existence of solutions for a class of Kirchhoff-type equations with indefinite potential

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Zhou ◽  
Yunshun Wu
Keyword(s):  
Morse Theory ◽  
Existence Of Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Indefinite Potential

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.

scholarly journals Multiplicity results for Kirchhoff type elliptic problems with Hardy potential

2019 ◽  
Vol 38 (4) ◽  
pp. 31-50
Author(s):  
M. Bagheri ◽  
Ghasem A. Afrouzi
Keyword(s):  
Local Minimum ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Hardy Potential ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Minimum Theorem

In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

scholarly journals Existence of solutions for a bi-nonlocal fractionalp-Kirchhoff type problem

2016 ◽  
Vol 71 (1) ◽  
pp. 255-266 ◽  
Author(s):  
Mingqi Xiang ◽  
Binlin Zhang ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Existence Of Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

Existence of solutions for a critical fractional Kirchhoff type problem in ℝ N

2017 ◽  
Vol 60 (9) ◽  
pp. 1647-1660 ◽  
Author(s):  
MingQi Xiang ◽  
BinLin Zhang ◽  
Hong Qiu
Keyword(s):  
Existence Of Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

scholarly journals Existence Results for apx-Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Existence Of Solutions ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Infinitely Many Solutions ◽  
Fountain Theorem ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity

We consider the existence and multiplicity of solutions for thepx-Kirchhoff-type equations without Ambrosetti-Rabinowitz condition. Using the Mountain Pass Lemma, the Fountain Theorem, and its dual, the existence of solutions and infinitely many solutions were obtained, respectively.

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