Hi there,(adsbygoogle = window.adsbygoogle || []).push({});

I'm an economics grad student and looking for a pointer to a theorem/paper that solves the problem below.

Here goes:

I have the system

[tex]\dot{B(i)} =- \int_0^J \alpha(i,t)(\pi(i,t)-B(i)-G(t))m(t) d t[/tex]

[tex]\dot{G(j)} =- \int_0^I \alpha(t,j)(\pi(t,j)-B(t)-G(j)w(t) d t[/tex]

with fixed boundary conditions on B(I) and G(J) (both strictly positive).

[tex]\pi[/tex] is twice cont. diff, m and w are from a uniformly equicontinuous set of functions on a closed interval, and [tex]\alpha[/tex] is the indicator function for the [tex] (\pi(i,j)-B(i)-G(j))[/tex] term being nonnegative. I can impose conditions on [tex]\pi[/tex] so that this expression is zero at only two points i or j for any given j or i (the functions are "strictly single-peaked" in each dimension).

I would need the solution (B*, G*) to this system to be continuous w.r.t. (m,w) (all with the sup norm). This is part of proving existence of an equilibrium (fixed point) for a larger system, in case you are wondering... if I forgot anything, please let me know. Any help is greatly appreciated. Honorable mention in my thesis/paper if successful!

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Continuity of DE solution in the _density functions_?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Continuity solution _density | Date |
---|---|

Let f(t) be piecewise continuous and of exponential order | May 3, 2015 |

Mathematical model of continuous and batch (discrete) system combined | Dec 11, 2012 |

Transform of a piecewise continuous function | Jun 1, 2012 |

Numerical solution of continuity equation, implicit scheme, staggered grid | Nov 29, 2011 |

Continuity of the blow up time | Apr 2, 2011 |

**Physics Forums - The Fusion of Science and Community**