Principal eigenvalue and maximum principle for cooperative periodic–parabolic systems
نویسندگان
چکیده
منابع مشابه
On Cooperative Elliptic Systems: Principal Eigenvalue and Characterization of the Maximum Principle
The purpose of this set of notes is to present the connection between the classical maximum principle with the principal eigenvalue of the elliptic operator. We will start with the maximum principle for single equations and proceed to the case of cooperative (or weakly-coupled) systems. By adopting an idea due to G. Sweers, we give a characterization of the principal eigenvalue for a cooperativ...
متن کاملMaximum Principle and generalized principal eigenvalue for degenerate elliptic operators
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem. The new notion of generalized principal eigenvalue that we introduce here al...
متن کاملAsymptotic Behavior of the Principal Eigenvalue for Cooperative Elliptic Systems and Applications
The asymptotic behavior of the principal eigenvalue for general linear cooperative elliptic systems with small diffusion rates is determined. As an application, we show that if a cooperative system of ordinary differential equations has a unique positive equilibrium which is globally asymptotically stable, then the corresponding reaction-diffusion system with either the Neumann boundary conditi...
متن کاملA maximum principle for some nonlinear cooperative elliptic PDE systems with mixed boundary conditions
One of the classical maximum principles state that any nonnegative solution of a proper elliptic PDE attains its maximum on the boundary of a bounded domain. We suitably extend this principle to nonlinear cooperative elliptic systems with diagonally dominant coupling and with mixed boundary conditions. One of the consequences is a preservation of nonpositivity, i.e. if the coordinate functions ...
متن کاملA Variational Principle for Eigenvalue Problems of Hamiltonian Systems
We consider the bifurcation problem u+λu = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue λ. We give a variational characterization of the bifurcating branch λ as a function of the amplitude of the solution. As an application we show how it can be used to obtain simple approximate closed formulae for the period of large amp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis
سال: 2019
ISSN: 0362-546X
DOI: 10.1016/j.na.2018.07.014