Existence of multiple solutions of Kirchhoff type equation with sign-changing potential

2014 ◽  
Vol 242 ◽  
pp. 491-499 ◽  
Author(s):  
Jian Zhang ◽  
Xianhua Tang ◽  
Wen Zhang
Keyword(s):  
Multiple Solutions ◽  
Type Equation ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

scholarly journals The Existence of Multiple Solutions for Nonhomogeneous Kirchhoff Type Equations in

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Qi Zhang ◽  
Xiaoli Zhu
Keyword(s):  
Multiple Solutions ◽  
Type Equation ◽  
Radial Solutions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

We are concerned with the existence of multiple solutions to the nonhomogeneous Kirchhoff type equation where are positive constants, , we can find a constant such that for all the equation has at least two radial solutions provided .

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.

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