Asymptotic Behavior of the Non-resonance Eigenvalues of the Fractional Schrödinger Operator with Neumann Condition
We present an analytical investigation of the asymptotic behavior of non-resonance eigenvalues for the fractional Schrödinger operator under homogeneous Neumann boundary conditions. Our findings reveal an intriguing convergence: as the system evolves, the eigenvalues of the fractional Schrödinger operator increasingly resemble those of the fractional Laplace operator. By deriving a precise asymptotic formula, we provide new insights into the spectral properties of these operators, highlighting their deeper connections and potential applications in mathematical physics.
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