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Multiple Solutions for Nonhomogeneous Schr\(\ddot{o}\)dinger Equations

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Abstract

In this article, we study the following nonhomogeneous Schr\(\ddot{o}\)dinger equation

$$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u=f(x,u)+k(x),\,\, \, x\in \mathbb {R}^{N}, \end{aligned}$$

where V(x) is a given positive potential. Under some suitable assumptions on V, f and k, the existence of multiple solutions is proved using the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.

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Funding

This work is partially supported by NNSF (No:11001274) of China.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Central South University, Changsha, People’s Republic of China

    Ruixi Liang & Tingting Shang

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  1. Ruixi Liang
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  2. Tingting Shang
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All authors jointly worked on the results, and they read and approved the final manuscript.

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Correspondence to Ruixi Liang.

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Liang, R., Shang, T. Multiple Solutions for Nonhomogeneous Schr\(\ddot{o}\)dinger Equations. Mediterr. J. Math. 18, 59 (2021). https://doi.org/10.1007/s00009-021-01702-y

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