Variational Approach for the Variable-Order Fractional Magnetic Schrödinger Equation with Variable Growth and Steep Potential in ℝN

Variational Approach for the Variable-Order Fractional Magnetic Schrödinger Equation with Variable Growth and Steep Potential in ℝN

In this paper, we show the existence of solutions for an indefinite fractional Schrödinger equation driven by the variable-order fractional magnetic Laplace operator involving variable exponents and steep potential. By using the decomposition of the Nehari manifold and variational method, we obtain...

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Veröffentlicht in:Advances in mathematical physics 2020, Vol.2020 (2020), p.1-15
Hauptverfasser: Wang, Yanning, Tian, Liping, Zhou, Bianxiang, Zhou, Jianwen
Format: Artikel
Sprache:eng
Schlagworte:
Decomposition
Hilbert space
Hypotheses
Inequality
Magnetic fields
Schrodinger equation
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Zusammenfassung:In this paper, we show the existence of solutions for an indefinite fractional Schrödinger equation driven by the variable-order fractional magnetic Laplace operator involving variable exponents and steep potential. By using the decomposition of the Nehari manifold and variational method, we obtain the existence results of nontrivial solutions to the equation under suitable conditions.
ISSN:1687-9120
1687-9139
DOI:10.1155/2020/1320635