Abstract
In this paper we present a unified approach to investigate existence and concentration of positive solutions for the following class of quasilinear Schrödinger equations,
where \(N\geqslant3, \varepsilon > 0, V(x)\) is a positive external potential,h is a real function with subcritical or critical growth. The problem is quite sensitive to the sign changing of the quasilinear term as well as to the presence of the parameter \(\gamma>0\). Nevertheless, by means of perturbation type techniques, we establish the existence of a positive solution \(u_{\varepsilon,\gamma}\) concentrating, as \(\varepsilon\rightarrow 0\), around minima points of the potential.
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The second-named author is supported by the Fundamental Research Funds for the Central Universities (No.2018MS59) and Natural Science Foundation of Guangdong (No.2018A0303130196). The third-named author was supported by NSFC(No.11871123).
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Cassani, D., Wang, Y. & Zhang, J. A Unified Approach to Singularly Perturbed Quasilinear Schrödinger Equations. Milan J. Math. 88, 507–534 (2020). https://doi.org/10.1007/s00032-020-00323-6
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DOI: https://doi.org/10.1007/s00032-020-00323-6