A multiplicity result for some nonlocal eigenvalue problem with exponential growth condition

2015 ◽  
Vol 125 ◽  
pp. 626-638 ◽  
Author(s):  
Sami Aouaoui
Keyword(s):  
Eigenvalue Problem ◽  
Growth Condition ◽  
Exponential Growth ◽  
Multiplicity Result ◽  
Nonlocal Eigenvalue Problem

scholarly journals A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction–Diffusion Systems with Fractional Reaction Rates

2003 ◽  
Vol 13 (06) ◽  
pp. 1529-1543 ◽  
Author(s):  
Juncheng Wei ◽  
Matthias Winter
Keyword(s):  
Eigenvalue Problem ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
The Stability ◽  
Nonlocal Eigenvalue Problem ◽  
Fractional Reaction

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction–diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray–Scott system, the hypercycle of Eigen and Schuster, angiogenesis, and the generalized Gierer–Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters.

ON A NONLOCAL EIGENVALUE PROBLEM AND ITS APPLICATIONS TO POINT-CONDENSATIONS IN REACTION–DIFFUSION SYSTEMS

2000 ◽  
Vol 10 (06) ◽  
pp. 1485-1496 ◽  
Author(s):  
JUNCHENG WEI
Keyword(s):  
Eigenvalue Problem ◽  
Single Point ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Stability And Instability ◽  
Nonlocal Eigenvalue Problem

We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in the Gierer–Meinhardt system and generalized Gray–Scott system. We give some sufficient conditions for stability and instability. The conditions are new and can be applied to the study of stability of single point-condensation solutions.

scholarly journals The eigenvalue problem for thep-Laplacian-like equations

2003 ◽  
Vol 2003 (9) ◽  
pp. 575-586 ◽  
Author(s):  
Zu-Chi Chen ◽  
Tao Luo
Keyword(s):  
Eigenvalue Problem ◽  
Smooth Domain ◽  
Multiplicity Result ◽  
Bounded Smooth Domain ◽  
Capillary Phenomena ◽  
Bounded Smooth

We consider the eigenvalue problem for the followingp-Laplacian-like equation:−div(a(|Du|p)|Du|p−2Du)=λf(x,u)inΩ,u=0on∂Ω, whereΩ⊂ℝnis a bounded smooth domain. Whenλis small enough, a multiplicity result for eigenfunctions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for applications of the theorems.

Some global results for a class of homogeneous nonlocal eigenvalue problems

2019 ◽  
Vol 21 (03) ◽  
pp. 1750093 ◽  
Author(s):  
Guowei Dai
Keyword(s):  
Eigenvalue Problem ◽  
Bifurcation Point ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Positive Answer ◽  
Spectral Structure ◽  
Type Problem ◽  
Bifurcation Phenomenon ◽  
Kirchhoff Type Problem ◽  
Nonlocal Eigenvalue Problem

This paper studies the global bifurcation phenomenon for the following homogeneous nonlocal eigenvalue problem [Formula: see text] Under some natural hypotheses on [Formula: see text] and [Formula: see text], we show that [Formula: see text] is a bifurcation point of the nontrivial solution set of the above problem. As application of the above result, we determine the interval of [Formula: see text], in which there exist positive solutions for the following Kirchhoff type problem [Formula: see text] where [Formula: see text] is asymptotically 3-linear at zero and infinity. Our results provide a positive answer to an open problem. Moreover, we also study the spectral structure for a homogeneous nonlocal eigenvalue problem.

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