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The Cauchy problem for nonlocal abstract Schrödinger equations and applications

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Abstract

Here, the Cauchy problem for linear and nonlinear nonlocal Schrödinger equations are studied. The equation involves a convolution integral operators with a general kernel operator functions whose Fourier transform are operator functions defined in a Hilbert space H together with some growth conditions. By assuming enough smoothness on the initial data and the operator functions, the local and global existence and uniqueness of solutions are established. We can obtain a different classes of nonlocal Schr ödinger equations by choosing the space H and linear operators, which occur in a wide variety of physical systems

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Authors and Affiliations

  1. Antalya Bilim University Dosemealti, Antalya, 07190, Turkey

    Veli B. Shakhmurov

  2. Linking of Research Centers, Azerbaijan State Economic University, Baku, AZ1001, Azerbaijan

    Veli B. Shakhmurov

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  1. Veli B. Shakhmurov
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Correspondence to Veli B. Shakhmurov.

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Shakhmurov, V.B. The Cauchy problem for nonlocal abstract Schrödinger equations and applications. Anal.Math.Phys. 11, 147 (2021). https://doi.org/10.1007/s13324-021-00574-5

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  • DOI: https://doi.org/10.1007/s13324-021-00574-5

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