## Differential and Integral Equations

- Differential Integral Equations
- Volume 9, Number 3 (1996), 607-618.

### Positive solutions to a system of periodic parabolic partial differential equations

Afshin Ghoreishi and Roger Logan

#### Abstract

We use the methods of [24, 15] to provide an extension of results presented in [7, 16, 24] to derive existence of positive solutions to a general system of periodic parabolic equations which arise in the study of population dynamics. We will consider the following system with mixed boundary conditions. $$ \begin{align} u_t(x,t)-d_1(x,t)\Delta u(x,t)&= u(x,t)M(x,t,u,v) \\ v_t(x,t)-d_2(x,t)\Delta v(x,t)&= v(x,t)N(x,t,u,v). \end{align} $$

#### Article information

**Source**

Differential Integral Equations, Volume 9, Number 3 (1996), 607-618.

**Dates**

First available in Project Euclid: 7 May 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367969975

**Mathematical Reviews number (MathSciNet)**

MR1371711

**Zentralblatt MATH identifier**

0852.35061

**Subjects**

Primary: 35K50

Secondary: 35B10: Periodic solutions 35K55: Nonlinear parabolic equations 35Q80: PDEs in connection with classical thermodynamics and heat transfer 92D25: Population dynamics (general)

#### Citation

Ghoreishi, Afshin; Logan, Roger. Positive solutions to a system of periodic parabolic partial differential equations. Differential Integral Equations 9 (1996), no. 3, 607--618. https://projecteuclid.org/euclid.die/1367969975