Results on the Existence and Multiplicity of Solutions for a Class of Sublinear Degenerate Schrödinger Equations in

In this paper, we study the existence and multiplicity of nontrivial solutions of the semilinear degenerate Schrödinger equation where is a potential function defined on and the nonlinearity is of sublinear growth and satisfies some appropriate conditions to be specified later. Here is an -elliptic...

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Bibliographic Details
Published in:Mathematical Notes 2022, Vol.112 (5-6), p.845-860
Main Author: My, Bui Kim
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Existence theorems
Fields (mathematics)
Mathematics
Mathematics and Statistics
Operators (mathematics)
Schrodinger equation
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Summary:In this paper, we study the existence and multiplicity of nontrivial solutions of the semilinear degenerate Schrödinger equation where is a potential function defined on and the nonlinearity is of sublinear growth and satisfies some appropriate conditions to be specified later. Here is an -elliptic operator with respect to a family of locally Lipschitz continuous vector fields. We apply the Ekeland variational principle and a version of the fountain theorem in the proofs of our main existence results. Our main results extend and improve some recent ones in the literature.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434622110190