Existence of infinitely many solutions for degenerate p-fractional Kirchhoff equations with critical Sobolev–Hardy nonlinearities

2017 ◽  
Vol 68 (6) ◽  
Author(s):  
Yueqiang Song ◽  
Shaoyun Shi
Keyword(s):  
Infinitely Many Solutions ◽  
Kirchhoff Equations

scholarly journals Multiple Solutions for Kirchhoff Equations under the Partially Sublinear Case

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Wenjun Feng ◽  
Xiaojing Feng
Keyword(s):  
Multiple Solutions ◽  
Infinitely Many Solutions ◽  
Kirchhoff Equations ◽  
Kirchhoff Type ◽  
Clark’S Theorem

We prove the infinitely many solutions to a class of sublinear Kirchhoff type equations by using an extension of Clark’s theorem established by Zhaoli Liu and Zhi-Qiang Wang.

scholarly journals Infinitely many solutions for the p-fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity

2018 ◽  
Vol 23 (4) ◽  
pp. 599-618
Author(s):  
Sihua Liang ◽  
Jihui Zhang
Keyword(s):  
Electromagnetic Fields ◽  
Mountain Pass Lemma ◽  
Infinitely Many Solutions ◽  
Concentration Compactness ◽  
Critical Nonlinearity ◽  
Kirchhoff Equations ◽  
Fractional Sobolev Space ◽  
Concentration Compactness Principle ◽  
Symmetric Mountain Pass Lemma ◽  
Compactness Principle

In this paper, we consider the fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity. By means of the concentration-compactness principle in fractional Sobolev space and the Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions, which tend to zero for suitable positive parameters.

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