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Infinitely many solutions for a gauged nonlinear Schrödinger equation. (English) Zbl 1411.35098

Summary: This paper is concerned with a gauged nonlinear Schrödinger equation \[ - \Delta u + \omega u + \left(\frac{h^2(| x |)}{| x |^2} + \int_{| x |}^\infty \frac{h(s)}{s} u^2(s) d s\right) u = f(| x |, u)\quad\text{in }\mathbb{R}^2 . \] Under some suitable conditions on the nonlinearity \(f\), we obtain two new existence results of infinitely many high energy solutions by using variational methods, and our results generalize and improve the recent result in the literature.

MSC:

35J10 Schrödinger operator, Schrödinger equation
35J20 Variational methods for second-order elliptic equations
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