Fractal Fract, Vol. 9, Pages 469: Normalized Ground States for Mixed Fractional Schrödinger Equations with Combined Local and Nonlocal Nonlinearities
Fractal and Fractional doi: 10.3390/fractalfract9070469
Authors:
Jie Yang
Haibo Chen
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 L2-critical case. For L2-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.
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Jie Yang www.mdpi.com