scholarly journals Existence and multiple solutions for the critical fractional $p$-Kirchhoff type problems involving sign-changing weight functions

Authorea ◽  
2020 ◽  
Author(s):  
Jie Yang ◽  
Senli Liu ◽  
Haibo Chen
Keyword(s):  
Multiple Solutions ◽  
Weight Functions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problems

Multiplicity results for elliptic Kirchhoff-type problems

2017 ◽  
Vol 6 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Sami Baraket ◽  
Giovanni Molica Bisci
Keyword(s):  
Weak Solutions ◽  
Multiple Solutions ◽  
Fractional Operators ◽  
Type Problem ◽  
Small Perturbations ◽  
Multiplicity Results ◽  
Nonlinear Part ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Type Problems

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.

Multiple solutions for Kirchhoff-type problems with variable exponent and nonhomogeneous Neumann conditions

2017 ◽  
Vol 291 (2-3) ◽  
pp. 326-342 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Anderson L. A. De Araujo ◽  
Ghasem A. Afrouzi ◽  
Shahin Moradi
Keyword(s):  
Multiple Solutions ◽  
Variable Exponent ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problems
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