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.

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