We exhibit existence of non-trivial solutions of some fractional linear Schr & ouml;dinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the presence of a Hardy potential.
Mainini, E., Ognibene, R., Volzone, B. (2025). Local multiplicity for fractional linear equations with Hardy potentials. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 64(2) [10.1007/s00526-024-02914-2].
Local multiplicity for fractional linear equations with Hardy potentials
Ognibene R.;
2025
Abstract
We exhibit existence of non-trivial solutions of some fractional linear Schr & ouml;dinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the presence of a Hardy potential.
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