Publication details
Semilinear elliptic equations with Hardy potential and subcritical source term
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007%2Fs00526-017-1144-6 |
| Doi | http://dx.doi.org/10.1007/s00526-017-1144-6 |
| Keywords | Hardy potential;Martin kernel;normalized boundary trace;source terms |
| Description | Let Omega be a smooth bounded domain in R-N (N > 2) and delta(x) := dist (x, partial derivative Omega).Assume mu is an element of R+ nu is a nonnegative finite measure on partial derivative Omega and g is an element of C(Omega x R+). We study positive solutions of -Delta u - mu/delta(2) u = g(x, u) in Omega, tr* (u) = nu. (P) Here tr*(u) denotes the normalized boundary trace of u which was recently introduced by Marcus and Nguyen (Ann Inst H Poincare Anal Non Lineaire, 34, 69- 88, 2017). We focus on the case 0 < mu < C-H(Omega) (the Hardy constant for Omega) and provide qualitative properties of positive solutions of (P). When g(x, u) = u(q) with q > 0, we prove that there is a critical value q* (depending only on N, mu) for (P) in the sense that if q < q* then (P) possesses a solution under a smallness assumption on., but if q >= q* this problem admits no solution with isolated boundary singularity. Existence result is then extended to a more general setting where g is subcritical [see (1.28)]. We also investigate the case where g is linear or sublinear and give an existence result for (P). |