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Nonexistence of solutions in $(0,1)$ for K-P-P-type equations
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http://ejde.math.txstate.edu/Abstract
Consider the KPP-type equation of the form $\Delta u+f(u)=0$, where $f:[0,1] \to \mathbb R_{+}$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$. The significance of this result from the point of view of probability theory is also discussed.
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