Publication details
On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF DIFFERENTIAL EQUATIONS |
| MU Faculty or unit | |
| Citation | |
| Web | Full Text |
| Doi | http://dx.doi.org/10.1016/j.jde.2018.07.060 |
| Keywords | Hardy potential;Semilinear equations;Elliptic systems;Boundary trace |
| Description | Let Omega subset of R-N (N >= 3) be a bounded C-2 domain and delta(x) = dist (x, partial derivative Omega). Put L-mu = Delta + mu/delta(2) with mu > 0. In this paper, we provide various necessary and sufficient conditions for the existence of weak solutions to -L(mu)u = u(p) + tau in Omega, u = nu on partial derivative Omega, where mu > 0, p > 0, tau and nu are measures on Omega and partial derivative Omega respectively. We then establish existence results for the system {-L(mu)u = is an element of v(p) + tau in Omega, -L(mu)v = is an element of u (p) over tilde + tau in Omega, u = nu, v = (nu) over tilde on partial derivative Omega, where is an element of = +/- 1, p > 0, (p) over tilde > 0, tau and (tau) over tilde are measures on Omega, nu and (nu) over tilde are measures on partial derivative Omega. We also deal with elliptic systems where the nonlinearities are more general. |