scholarly journals Multiple solutions to the nonhomogeneous Kirchhoff type problem involving a nonlocal operator

2016 ◽  
pp. 367-375
Author(s):  
Wenjing Chen ◽  
Jun ui Xie
Keyword(s):  
Multiple Solutions ◽  
Nonlocal Operator ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

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.

A critical Kirchhoff type problem involving a nonlocal operator

2014 ◽  
Vol 94 ◽  
pp. 156-170 ◽  
Author(s):  
Alessio Fiscella ◽  
Enrico Valdinoci
Keyword(s):  
Nonlocal Operator ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

scholarly journals Multiple solutions of the Kirchhoff-type problem in RN

2016 ◽  
Vol 1 (1) ◽  
pp. 229-238 ◽  
Author(s):  
Jiahua Jin
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Principle ◽  
Multiple Solutions ◽  
Mountain Pass Theorem ◽  
Nonlinear Partial Differential Equation ◽  
Point Theory ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

AbstractIn this paper, we concern with a class of quasilinear Kirchhoff-type problem. By using the Ekeland’s Variational Principle and Mountain Pass Theorem, the existence of multiple solutions is obtained. Besides, we also take this problem as an example to give the main frame of using critical point theory to find the weak solutions of nonlinear partial differential equation.

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