scholarly journals Existence results for a Kirchhoff-type equation involving fractional $ p(x) $-Laplacian

2021 ◽  
Vol 6 (8) ◽  
pp. 8390-8403
Author(s):  
Jinguo Zhang ◽  
◽  
Dengyun Yang ◽  
Yadong Wu
Keyword(s):  
Type Equation ◽  
Existence Results ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

Existence results for a Kirchhoff type equation in Orlicz–Sobolev spaces

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
EL Miloud Hssini ◽  
Najib Tsouli ◽  
Mustapha Haddaoui
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Nonlocal Problems ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

AbstractIn this paper, based on the mountain pass theorem and Ekeland’s variational principle, we show the existence of solutions for a class of non-homogeneous and nonlocal problems in Orlicz–Sobolev spaces.

scholarly journals Multiple solutions for a Kirchhoff-type equation with general nonlinearity

2018 ◽  
Vol 7 (3) ◽  
pp. 293-306 ◽  
Author(s):  
Sheng-Sen Lu
Keyword(s):  
Variational Methods ◽  
Multiple Solutions ◽  
Type Equation ◽  
Existence Results ◽  
Point Of View ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
General Nonlinearity

AbstractThis paper is devoted to the study of the following autonomous Kirchhoff-type equation: -M\biggl{(}\int_{\mathbb{R}^{N}}|\nabla{u}|^{2}\biggr{)}\Delta{u}=f(u),\quad u% \in H^{1}(\mathbb{R}^{N}),where M is a continuous non-degenerate function and {N\geq 2}. Under suitable additional conditions on M and general Berestycki–Lions-type assumptions on the nonlinearity of f, we establish several existence results of multiple solutions by variational methods, which are also naturally interpreted from a non-variational point of view.

scholarly journals Solutions of Nonlocal -Laplacian Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mustafa Avci ◽  
Rabil Ayazoglu (Mashiyev)
Keyword(s):  
Laplace Operator ◽  
Variational Approach ◽  
Nonlocal Problem ◽  
Type Equation ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Equation ◽  
Laplacian Equations

In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

scholarly journals On a fractional Kirchhoff-type equation via Krasnoselskii’s genus

2015 ◽  
Vol 94 (3-4) ◽  
pp. 347-361 ◽  
Author(s):  
Giovany M. Figueiredo ◽  
Giovanni Molica Bisci ◽  
Raffaella Servadei
Keyword(s):  
Type Equation ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation
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