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Results on the Existence and Multiplicity of Solutions for a Class of Sublinear Degenerate Schrödinger Equations in \(\mathbb{R}^N\)

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Abstract

In this paper, we study the existence and multiplicity of nontrivial solutions of the semilinear degenerate Schrödinger equation

$$-\mathcal{L}u + V(x)u = f(x,u),\qquad x\in \mathbb{R}^N,\quad N\ge 3,$$

where \(V\) is a potential function defined on \(\mathbb{R}^N\) and the nonlinearity \(f\) is of sublinear growth and satisfies some appropriate conditions to be specified later. Here \(\mathcal{L}\) is an \(X\)-elliptic operator with respect to a family \(X = \{X_1, \ldots, X_m\}\) 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.

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  1. Hanoi Pedagogical University 2, Vinh Phuc, 283460, Vietnam

    Bui Kim My

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My, B.K. Results on the Existence and Multiplicity of Solutions for a Class of Sublinear Degenerate Schrödinger Equations in \(\mathbb{R}^N\). Math Notes 112, 845–860 (2022). https://doi.org/10.1134/S0001434622110190

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  • DOI: https://doi.org/10.1134/S0001434622110190

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