 Abstract | This thesis contains a discussion of logistic equations with di usion, impulses
and time delays both discrete and continuous type. The boundary conditions
used in these problems are Dirichlet, Neumann and Robin boundary
conditions. Both single and multi species logistic equations are investigated.
The impulse times employed here are the xed ones. Some results on the
problems are:
(1) Single species logistic equation with diusion, impulses, discrete delay,
Dirichlet and Robin boundary conditions.
- Existence and uniqueness of solution:
{ Dirichlet boundary case(Corollary 3.1).
{ Robin boundary case(Corollary 3.2).
- Conditions for the existence of zero attractor (Theorem 3.9).
- Conditions for the existence of positive attractor (Theorem 3.11).
(2) Logistic equation with di usion, impulses, continuous delay and Neumann
boundary condition.
- Single species: existence and uniqueness of solution (Theorem
4.1).
- Single species: conditions for the existence of zero attractors
(Theorem 4.2).
- Single species: conditions for the existence of positive attractor
(Theorem 4.3).
- Multi species: conditions for the existence of positive attractor
(Theorem 4.4).
This thesis is organised as follows: in Chapter 2, the background of these
problems is presented. Chapter 3 is concerned with the existence and uniqueness
of solution, zero and positive attractor of logistic equations with di usion,
impulses, discrete time delay, and Dirichlet and Robin boundary conditions.
We discuss the existence and uniqueness of solution of di usive logistic equations
with distributed delay, impulses and Neumann boundary condition, zero
and positive attractors in Chapter 4. Some conditions to obtain a positive
attractor for multi species logistic equation with di usion, distributed delay,
impulses and Neumann boundary condition are presented in the last section
of Chapter 4. |
