| Abstract: |
| We study elliptic equations of the form \( (-\Delta)^{\frac{\alpha}{2}} u = f(x,u)\) in \(\mathbb{R}^{n}\),
where \((-\Delta)^{\frac{\alpha}{2}}\) denotes the fractional Laplacian in \(\mathbb{R}^{n}\) for \( 0 < \alpha < n \)
and \(n \geq 2\). The nonlinearity \(f(x,u) = \sum_{i=1}^{M} \sigma_{i} u^{q_i} + \omega\) includes sublinear growth terms,
with \( 0 < q_i < 1\), the coefficients \(\sigma_{i}\) and the data \(\omega\) are Radon measures on \(\mathbb{R}^n\).
We will present results on the existence, uniqueness, and pointwise estimates for some classes of solutions to these problems.
This talk is based on joint work with Kentaro Hirata, Aye Chan May, Toe Toe Shwe, and Igor E. Verbitsky. |
|