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Mixed Concave–Convex Sub-Superlinear Schrödinger Equation: Survey and Development of Some New Cases

In: Nonlinear Analysis and Global Optimization

Author

Listed:
  • Riadh Chteoui

    (University of Monastir
    University of Tabuk)

  • Anouar Ben Mabrouk

    (University of Monastir
    University of Tabuk
    University of Kairouan)

  • Carlo Cattani

    (Tuscia University)

Abstract

The present chapter is concerned with a whole review of the well known Schrödinger equation in a mixed case of nonlinearities. We precisely consider a general nonlinear model characterized by a superposition of linear, sub-linear, super-linear sometimes concave–convex power laws on the form f(u) = |u|p−1 u ±|u|p−1 u. In a first part, we develop theoretical results on existence, uniqueness, classification as well as the behavior of the solutions of the ground state radial problem according to the power laws and the initial value. Next, in a second part, some examples are developed with graphical illustrations to confirm the theoretical results exposed previously. The graphs show coherent states between the theoretical findings and the numerical illustrations.The chapter in its whole aim is a review of existing results about the studied problems reminiscent of some few cases that are not previously developed. We aim thus it will constitute a good reference especially for beginners in the field of nonlinear analysis of PDEs.

Suggested Citation

  • Riadh Chteoui & Anouar Ben Mabrouk & Carlo Cattani, 2021. "Mixed Concave–Convex Sub-Superlinear Schrödinger Equation: Survey and Development of Some New Cases," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 109-162, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-61732-5_5
    DOI: 10.1007/978-3-030-61732-5_5
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    35J25; 35J60;

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