Preprint

Inserted: 1 jan 2024
Last Updated: 22 jan 2024

Pages: 19
Year: 2024

Abstract:

We get multiplicity of normalized solutions for the fractional Schrödinger equation (−∆)^s u + V (εx)u = λu + h(εx)f (u) in R N , \int u² dx = a, where (−∆)^s is the fractional Laplacian, s ∈ (0, 1), a, ε > 0, λ ∈ R is an unknown parameter that appears as a Lagrange multiplier, V, h : R N → [0, +∞) are bounded and continuous, and f is continuous function with subcritical growth. We prove that the numbers of normalized solutions are at least the numbers of global maximum points of h when ε is small enough.

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