Advances in Differential Equations

Positive periodic solutions for semilinear reaction diffusion systems on $\bf {R}^N$

Sandro Merino

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The existence and nonexistence of positive time-periodic solutions of semilinear reaction diffusion systems of the type $$ \begin{cases} \partial_{t}u +\mathcal{A}_{1}u = au-bg_{1}(u)u - h_{1}(u,v)u\\ \partial_{t}v +\mathcal{A}_{2}v = dv-fg_{2}(v)v + h_{2}(u)v \end{cases} \quad \text{ in } \ \mathbb{r}^{N}\times (0,\infty ), $$ is discussed. Here the coefficients $a,b,d,f,$ and the coupling terms $g_{1},g_{2},h_{1},h_{2}$ depend on space and time and satisfy suitable conditions. The differential operators $\mathcal{A}_{1}$ and $\mathcal{A}_{2}$ are elliptic with space- and time-dependent coefficients. In particular, the time dependence is always assumed to be periodic with a fixed common period. A topological method, based on the Leray-Schauder degree, is used to obtain the existence of positive time-periodic solutions. Finally, we apply our results to various population models.

Article information

Adv. Differential Equations Volume 1, Number 4 (1996), 579-609.

First available in Project Euclid: 25 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35B10: Periodic solutions 92D25: Population dynamics (general)


Merino, Sandro. Positive periodic solutions for semilinear reaction diffusion systems on $\bf {R}^N$. Adv. Differential Equations 1 (1996), no. 4, 579--609.

Export citation