Publication details
Schrödinger equations with singular potentials: linear and nonlinear boundary value problems
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Mathematische Annalen |
| MU Faculty or unit | |
| Citation | |
| Web | Full Text |
| Doi | http://dx.doi.org/10.1007/s00208-018-1734-4 |
| Keywords | Hardy potential; Martin kernel; moderate solutions; normalized boundary trace; critical exponent; good measures |
| Description | Let RN (N3) be a C2 bounded domain and F< subset of> be a C2 submanifold with dimension 0kN-2. Denote F=(,F), V=F-2and CH(V) the Hardy constant relative to V in . We study positive solutions of equations (LE) -LVu=0 and (NE) -LVu+f(u)=0 in where LV=+V, CH(V) and fC(R) is an odd, monotone increasing function. We extend the notion of normalized boundary trace introduced in Marcus and Nguyen (Ann Inst H. Poincare (C) Non Linear Anal 34:69-88, 2015) and employ it to investigate the linear equation (LE). Using these results we obtain properties of moderate solutions of (NE). Finally we determine a criterion for subcriticality of points on relative to f and study b.v.p. for (NE). In particular we establish existence and stability results when the data is concentrated on the set of subcritical points. |