Global behavior for a diffusive predator-prey model with stage structure and nonlinear density restriction. I: The case in .
We discuss the discrete -Laplacian eigenvalue problem, where is a given positive integer and , . First, the existence of an unbounded continuum of positive solutions emanating from is shown under suitable conditions on the nonlinearity. Then, under an additional condition, it is shown that the positive solution is unique for any and all solutions are ordered. Thus the continuum is a monotone continuous curve globally defined for all .
We describe the global dynamics of a disease transmission model between two regions which are connected via bidirectional or unidirectional transportation, where infection occurs during the travel as well as within the regions. We define the regional reproduction numbers and the basic reproduction number by constructing a next generation matrix. If the two regions are connected via bidirectional transportation, the basic reproduction number characterizes the existence of equilibria as well as...
In this paper Zadunaisky's technique is used to estimate the global error propagated in the numerical solution of the system of retarded differential equations by Euler's method. Some numerical examples are given.
In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
We prove global existence and stability results for a semilinear parabolic equation, a semilinear functional equation and a semilinear integral equation using an inequality which may be viewed as a nonlinear singular version of the well known Gronwall and Bihari inequalities.