Multiplicity of solutions for Kirchhoff type equations involving critical Sobolev exponents in high dimension

2016 ◽  
Vol 39 (13) ◽  
pp. 3722-3734 ◽  
Author(s):  
Xianzhong Yao ◽  
Chunlai Mu
Keyword(s):  
High Dimension ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Critical Sobolev Exponents

scholarly journals Multiplicity of Solutions for Nonlocal Elliptic System of(p,q)-Kirchhoff Type

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Bitao Cheng ◽  
Xian Wu ◽  
Jun Liu
Keyword(s):  
Elliptic System ◽  
Critical Points ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Periodic Condition ◽  
Kirchhoff Type ◽  
Three Critical Points Theorem ◽  
Palais Smale Condition

This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff type−[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω,−[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω,u=v=0, on∂Ω.Under bounded condition onMand some novel and periodic condition onF, some new results of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained by means of Bonanno's multiple critical points theorems without the Palais-Smale condition and Ricceri's three critical points theorem, respectively.

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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