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 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 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 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

scholarly journals On the existence of solutions to a fourth-order quasilinear resonant problem

2002 ◽  
Vol 7 (3) ◽  
pp. 125-133 ◽  
Author(s):  
Shibo Liu ◽  
Marco Squassina
Keyword(s):  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Morse Theory ◽  
Existence Of Solutions ◽  
Nontrivial Solutions ◽  
Navier Boundary Conditions ◽  
Resonant Problem

By means of Morse theory we prove the existence of a nontrivial solution to a superlinearp-harmonic elliptic problem with Navier boundary conditions having a linking structure around the origin. Moreover, in case of both resonance near zero and nonresonance at+∞the existence of two nontrivial solutions is shown.

scholarly journals Multiplicity of positive solutions for critical fractional Kirchhoff type problem with concave-convex nonlinearity

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3791-3798
Author(s):  
Chang-Mu Chu ◽  
Zhi-Peng Cai ◽  
Hong-Min Suo
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Multiplicity Of Positive Solutions

This paper is devoted to study a class of Kirchhoff type problem with critical fractional exponent and concave nonlinearity. By means of variational methods, the multiplicity of the positive solutions to this problem is obtained.

scholarly journals A Kirchhoff-type problem involving concave-convex nonlinearities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuan Gao ◽  
Lishan Liu ◽  
Shixia Luan ◽  
Yonghong Wu
Keyword(s):  
Energy Level ◽  
Variational Methods ◽  
Ground State ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
State Solution ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Least Energy

AbstractA Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

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