## Journals

- Advances in Mathematics of Communications
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CPAA

A generic semilinear equation in a star-shaped ring is considered. Any
solution bounded between its boundary values is shown to be decreasing along
rays starting from the origin, provided that a structural condition is
satisfied. A corresponding property for the product between the solution and a
(positive) power of $|x|$ is also investigated. Applications to the
Emden-Fowler and the Liouville equation are developed.

PROC

We study maximization and minimization problems for the energy integral of
a sub-linear $p$-Laplace equation in a domain $\Omega$, with weight $\chi_D$, where $D\subset\Omega$
is a variable subset with a fixed measure $\alpha$.
We prove Lipschitz continuity for the energy integral of a maximizer and differentiability for the
energy integral of the minimizer with respect to $\alpha$.

CPAA

We prove that the initial-value problem for the fractional heat equation admits an entire solution provided that the (possibly unbounded) initial datum has a conveniently moderate growth at infinity. Under the same growth condition we also prove that the solution is unique. The result does not require any sign assumption, thus complementing the Widder's type theorem of Barrios et al.[

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