On a singular elliptic problem with variable exponent
DOI:
https://doi.org/10.24193/subbmath.2023.1.03Keywords:
singular elliptic problem, variable exponent, variational methods.Abstract
In the present note we study a semilinear elliptic Dirichlet problem involving a singular term with variable exponent of the following type
$$
\left\{
\begin{array}{ll}
-\Delta u= \frac{f(x)}{u^{\gamma(x)} }, & \mbox{ in }\Omega, \\
u>0, & \mbox{ in }\Omega, \\
u=0, & \mbox{ on }\partial \Omega.
\end{array}
\right.
$$
Existence and uniqueness results are proved when \(f\geq 0\).
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