The existence and multiplicity of $L^2$-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

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The existence and multiplicity of \(L^2\)-normalized solutions to nonlinear Schrödinger equations with variable coefficients