Electron. J. Diff. Equ., Vol. 2013 (2013), No. 124, pp. 1-3.

Existence and uniqueness of a local solution for $x' = f(t,x)$ using inverse functions

Jeffrey T. Hoag

Abstract:
A condition on the function f is given such that the scalar ordinary differential equation $x' = f(t,x)$ with initial condition $x(t_0) = x_0$ has a unique solution in a neighborhood of $t_0$. An example illustrates that this result can be used when other theorems which put conditions on the difference $f(t,x)-f(t,y)$ do not apply.

Submitted January 13, 2013. Published May 20, 2013.
Math Subject Classifications: 34A12.
Key Words: Existence; uniqueness; ordinary differential equation.

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Jeffrey T. Hoag
Mathematics Department
Providence College
Providence, RI 02918, USA
email: jhoag@providence.edu

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