| Abstract: |
| This talk presents new existence, non-existence and uniqueness results for the following problem
\[
L_{\Delta} u = f(x,u) \ \text{in} \ \Omega, \quad u = 0 \ \text{in} \ \mathbb{R}^N \setminus \Omega
\]
where $L_\Delta$ is the Logarithmic Laplace operator and $f$ satisfies sub-critical, critical and super-critical nonlinearities growth conditions. Such type of problems are connected to the model problems in population dynamics, optimal control, approximation of fractional harmonic maps, and fractional image
denoising. |
|