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Normalized Ground States for Mixed Fractional Schrödinger Equations with Combined Local and Nonlocal Nonlinearities

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Publicado en:Fractal and Fractional vol. 9, no. 7 (2025), p. 469-497
Autor principal: Yang, Jie
Otros Autores: Chen, Haibo
Publicado:
MDPI AG
Materias:
Parameter identification
Lagrange multiplier
Ground state
Regularity
Schrodinger equation
Variational methods
Nonlinearity
Acceso en línea:Citation/Abstract
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Resumen:This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Pohozaev identities, and prove the existence of radial, decreasing ground states, while showing nonexistence in the <inline-formula>L2</inline-formula>-critical case. For <inline-formula>L2</inline-formula>-supercritical exponents, we identify parameter regimes where ground states exist, characterized by a negative Lagrange multiplier. The analysis combines variational methods, scaling techniques, and the careful study of fibering maps to address challenges posed by competing nonlinearities and nonlocal interactions.
ISSN:2504-3110
DOI:10.3390/fractalfract9070469
Fuente:Engineering Database