Publication details

On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials


GKIKAS Konstantinos T. NGUYEN Phuoc-Tai

Year of publication 2019
Type Article in Periodical
MU Faculty or unit

Faculty of Science

Web Full Text
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.

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