Existence and multiplicity of solutions for Kirchhoff-type equation with radial potentials in $${\mathbb{R}^{3}}$$ R 3

2015 ◽  
Vol 66 (6) ◽  
pp. 3147-3158 ◽  
Author(s):  
Anran Li ◽  
Jiabao Su
Keyword(s):  
Type Equation ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Equation

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 𝓅 ( x ) -Kirchhoff-type equation involving 𝓅 ( x ) -biharmonic operator via genus theor

2020 ◽  
Vol 72 (6) ◽  
pp. 842-851
Author(s):  
S. Taarabti ◽  
Z. El Allali ◽  
K. Ben Haddouch
Keyword(s):  
Weak Solutions ◽  
Variational Approach ◽  
Type Equation ◽  
Biharmonic Operator ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Genus Theory ◽  
Kirchhoff Type Equation ◽  
Kirchhoff Type Problem

UDC 517.9 The paper deals with the existence and multiplicity of nontrivial weak solutions for the 𝓅 ( x ) -Kirchhoff-type problem, u = Δ u = 0 o n ∂ Ω . By using variational approach and Krasnoselskii’s genus theory, we prove the existence and multiplicity of solutions for the 𝓅 ( x ) -Kirchhoff-type equation.

scholarly journals Existence Results for apx-Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Existence Of Solutions ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Infinitely Many Solutions ◽  
Fountain Theorem ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity

We consider the existence and multiplicity of solutions for thepx-Kirchhoff-type equations without Ambrosetti-Rabinowitz condition. Using the Mountain Pass Lemma, the Fountain Theorem, and its dual, the existence of solutions and infinitely many solutions were obtained, respectively.

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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