Published Paper

Inserted: 1 apr 2025
Last Updated: 20 apr 2026

Journal: Calc. Var. Partial Differential Equations
Volume: 65
Number: 5
Year: 2026
Doi: 10.1007/s00526-026-03312-6

Abstract:

We investigate normalized solutions for doubly nonlinear Schr\"odinger equations on the real line with a defocusing standard nonlinearity and a focusing nonlinear point interaction of $\delta$--type at the origin. We provide a complete characterization of existence and uniqueness for normalized solutions and for energy ground states for every value of the nonlinearity powers. We show that the interplay between a defocusing standard and a focusing point nonlinearity gives rise to new phenomena with respect to those observed with single nonlinearities, standard combined nonlinearities, and combined focusing standard and pointwise nonlinearities.

Keywords: art. 143, 29 pp