Signed and sign‐changing solutions for a Kirchhoff‐type problem involving the fractional p ‐Laplacian with critical Hardy nonlinearity

2019 ◽  
Vol 43 (2) ◽  
pp. 968-995
Author(s):  
Rodrigo F. Gabert ◽  
Rodrigo S. Rodrigues
Keyword(s):  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Sign Changing Solutions

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 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.

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