On a singular elliptic problem with variable exponent

Francesca Faraci


In the present note we study a semilinear elliptic Dirichlet problem involving a singular term  with variable exponent of the following type

-\Delta u= \frac{f(x)}{u^{\gamma(x)} }, & \mbox{ in }\Omega, \\
u>0, & \mbox{ in }\Omega, \\
u=0, & \mbox{ on }\partial \Omega.

Existence and uniqueness results are proved when \(f\geq 0\).


singular elliptic problem; variable exponent; variational methods.

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DOI: http://dx.doi.org/10.24193/subbmath.2023.1.03


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