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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Gkikas, Konstantinos T.¹  Phuoc-Tai Nguyen² 

[1] Univ Chile, CNRS, UMI 2807, Ctr Modelamiento Matemat, Casilla 170 Correo 3, Santiago, Chile

[2] Masaryk Univ, Dept Math & Stat, Brno, Czech Republic

关键词: Hardy potential;    Semilinear equations;    Elliptic systems;    Boundary trace;   

DOI  :  10.1016/j.jde.2018.07.060

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free