Informace o publikaci

Schrödinger equations with singular potentials: linear and nonlinear boundary value problems



Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Mathematische Annalen
Fakulta / Pracoviště MU

Přírodovědecká fakulta

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Klíčová slova Hardy potential; Martin kernel; moderate solutions; normalized boundary trace; critical exponent; good measures
Popis 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.