# Browder–Minty theorem

In mathematics, the **Browder–Minty theorem** states that a bounded, continuous, coercive and monotone function *T* from a real, separable reflexive Banach space *X* into its continuous dual space *X*^{∗} is automatically surjective. That is, for each continuous linear functional *g* ∈ *X*^{∗}, there exists a solution *u* ∈ *X* of the equation *T*(*u*) = *g*. (Note that *T* itself is not required to be a linear map.)

## See also

- Pseudo-monotone operator; pseudo-monotone operators obey a near-exact analogue of the Browder–Minty theorem.

## References

- Renardy, Michael & Rogers, Robert C. (2004).
*An introduction to partial differential equations*. Texts in Applied Mathematics 13 (Second ed.). New York: Springer-Verlag. p. 364. ISBN 0-387-00444-0. (Theorem 10.49)

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