## A strong maximum principle for some quasilinear elliptic equations.(English)Zbl 0561.35003

The main result is the following maximum principle: if $$\beta$$ is a real- valued, non-decreasing function of a real variable with $$\beta (0)=0$$, and f is non-negative almost everywhere on $$\Omega \subset {\mathbb{R}}^ n$$, then every non-negative weak solution of $$-\Delta u+\beta (u)=f$$ is positive everywhere if and only if $$\int (\beta (s)s)^{-1/2}ds$$ diverges at $$s=0+$$. The result extends to certain quasi-linear equations.
Reviewer: J.F.Toland

### MSC:

 35B50 Maximum principles in context of PDEs 35J60 Nonlinear elliptic equations 35K55 Nonlinear parabolic equations
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### References:

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