Nonlinear Diff. Equ.

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1 total messages Started by Li Ziqing Thu, 10 Sep 1992 00:51

#62

Author: Li Ziqing
Date: Thu, 10 Sep 1992 00:51

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Hi, there

I have a question on the existance and uniqueness of the
following nonlinear differential equation

        f(x) - C d [f'(x) h(f'(x))] /dx =g(x)

where C>0 is a constant, g(x) is a known, piecewise C^0
continuous function and h(.) is a nonlinear function satisfying

(1) h(z) is C^1 continuous for all real z
(2) h is even h(z)=h(-z),
(3) h(z) >0,
(4) h(z) < 0 for all z > 0 and
(5) z h(z) --> 0 as z --> infinity

Examples of h(z) are

        exp(-z^2/sigma), 1/(1+z^2/sigma)

where sigma>0 is a constant.

Are there any mathematicians or engineers out there who have
any ideas about the existance and uniqueness of the above equation?

Any replies are greatly appreciated.


Z. Li

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