Hopf bifurcation for a delayed predator–prey diffusion system with Dirichlet boundary condition

2017 ◽  
Vol 311 ◽  
pp. 1-18 ◽  
Author(s):  
Zhan-Ping Ma ◽  
Hai-Feng Huo ◽  
Hong Xiang
Keyword(s):  
Boundary Condition ◽  
Hopf Bifurcation ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Diffusion System ◽  
Predator Prey

scholarly journals Positive Solutions of a Diffusive Predator-Prey System including Disease for Prey and Equipped with Dirichlet Boundary Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoqing Wen ◽  
Yue Chen ◽  
Hongwei Yin
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Disease Spread ◽  
Dimensional System ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fixed Point Index Theory

We study a three-dimensional system of a diffusive predator-prey model including disease spread for prey and with Dirichlet boundary condition and Michaelis-Menten functional response. By semigroup method, we are able to achieve existence of a global solution of this system. Extinction of this system is established by spectral method. By using bifurcation theory and fixed point index theory, we obtain existence and nonexistence of inhomogeneous positive solutions of this system in steady state.

Stability and Bifurcation in a Diffusive Logistic Population Model with Multiple Delays

2015 ◽  
Vol 25 (08) ◽  
pp. 1550107 ◽  
Author(s):  
Shanshan Chen ◽  
Junjie Wei
Keyword(s):  
Boundary Condition ◽  
Hopf Bifurcation ◽  
Dirichlet Boundary Condition ◽  
Population Model ◽  
Dirichlet Boundary ◽  
Positive Equilibrium ◽  
Multiple Delays ◽  
Stability And Bifurcation ◽  
The Stability

A diffusive logistic population model with multiple delays and Dirichlet boundary condition is considered in this paper. The stability/instability of the positive equilibrium and delay induced Hopf bifurcation are investigated. Moreover, we show which kind of delay could actually affect the dynamics.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS

2014 ◽  
Vol 66 (5) ◽  
pp. 1110-1142
Author(s):  
Dong Li ◽  
Guixiang Xu ◽  
Xiaoyi Zhang
Keyword(s):  
Boundary Condition ◽  
Fundamental Solution ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Obstacle Problem ◽  
Dirichlet Boundary ◽  
Radial Symmetry ◽  
Well Posedness ◽  
Robust Algorithm ◽  
Dispersive Estimate

AbstractWe consider the obstacle problem for the Schrödinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrödinger propagator and give a robust algorithm to prove sharp L1 → L∞ dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well–posedness and scattering for defocusing energy-critical NLS on with Dirichlet boundary condition and radial data in these dimensions.

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