Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with nonlinear boundary conditions

2020 ◽  
Author(s):  
Somayeh Yazdani ◽  
Ghasem Alizadeh Afrouzi ◽  
Jamal Rezaee Roshan ◽  
Sayyed Hashem Rasouli
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Kirchhoff Type Problems

scholarly journals MULTIPLICITY OF POSITIVE SOLUTIONS UNDER NONLINEAR BOUNDARY CONDITIONS FOR DIFFUSIVE LOGISTIC EQUATIONS

2004 ◽  
Vol 47 (2) ◽  
pp. 495-512 ◽  
Author(s):  
Kenichiro Umezu
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Elliptic Boundary ◽  
Nonlinear Boundary Conditions ◽  
Elliptic Boundary Value ◽  
Logistic Equations ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this paper we consider the existence and multiplicity of positive solutions of a nonlinear elliptic boundary-value problem with nonlinear boundary conditions which arises in population dynamics. While bifurcation problems from lines of trivial solutions are studied, the existence of bifurcation positive solutions from infinity is discussed. The former will be caught by the reduction to a bifurcation equation following the Lyapunov and Schmidt procedure. The latter will be based on a variational argument depending on the corresponding constrained minimization problem.AMS 2000 Mathematics subject classification: Primary 35J65; 35J20; 35P30; 35B32; 92D25

scholarly journals On the Existence of Nontrivial Solutions for Nonlocal Elliptic Kirchhoff Type Problems with Nonlinear Boundary Conditions

2015 ◽  
Vol 55 (1) ◽  
pp. 183-188
Author(s):  
S. H. Rasouli ◽  
B. Salehi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Type Equation ◽  
Nonlinear Boundary Conditions ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Kirchhoff Type Problems

Abstract In this paper, by using the Mountain Pass Lemma, we study the existence of nontrivial solutions for a nonlocal elliptic Kirchhoff type equation together with nonlinear boundary conditions.

scholarly journals Existence and Multiplicity of Positive Solutions for Kirchhoff-Type Equations with the Critical Sobolev Exponent

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Junjun Zhou ◽  
Xiangyun Hu ◽  
Tiaojie Xiao
Keyword(s):  
Critical Exponent ◽  
Positive Solutions ◽  
Mountain Pass Theorem ◽  
Critical Sobolev Exponent ◽  
Mountain Pass ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Sobolev Exponent ◽  
Multiplicity Of Positive Solutions ◽  
Kirchhoff Type Problems

In this paper, we consider the following Kirchhoff-type problems involving critical exponent −a+b∫Ω∇u2dxΔu+Vxu=μu2∗−1+λgx,u, x∈Ωu>0, x∈Ωu=0, x∈∂Ω. The existence and multiplicity of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth are studied under some suitable assumptions on Vx and gx,u. By using the mountain pass theorem and Brézis–Lieb lemma, the existence and multiplicity of positive solutions are obtained.

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