Suppose $A$, $B$, $C$ and $D$ are fixed arbitrary positive numbers.
I am free to choose $\epsilon$, $\epsilon_1$ and $\epsilon_2$ but they must be positive.
Can I choose the epsilons so that $\left((A -\frac{1}{\epsilon_1} - \frac{B}{2\epsilon_2})\frac{C\epsilon}{(1+\epsilon)} - \epsilon_1 D\right) > 0?$
I need this to show coercivity of a bilinear form.. Thanks.
I did some calculations, and it seems if I make $\epsilon_1$ very small and $\frac{\epsilon}{1+\epsilon}$ small then it might work but I can't prove it. Anyway I really hope it can be done.
Thanks