Lotka-Volterra with periodic coefficients differential inequality

Sep 2019
4
0
Poland
I would like to ask which transformation should I use to recive from this Lotka-Volterra inequality
\(\displaystyle x′=x(a−bx−cy)<x(a−bx),\)
this differential form
\(\displaystyle x(t)\leq \frac{x(T)e^{A(t)}}{1+x(T)\int \limits_{T}^{t}e^{A(s)}b(s)ds}, \text{where} A(t)=\int_T^t a(s)ds.\)
 
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