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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 9
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Research Article

Ground state solutions for modified quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory

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Pages 3182-3191 | Received 04 Aug 2020, Accepted 01 Oct 2020, Published online: 20 Oct 2020
 

Abstract

In this paper, we study the following modified quasilinear Schrödinger equation Δu+V(x)uκuΔ(u2)+qh2(|x|)|x|2(1+κu2)u+q|x|+h(s)s(2+κu2(s))u2(s)dsu=|u|p2uin R2, where κ>0, q>0, p>6 and VC(R2,R). We develop a more direct and simpler approach to prove the existence of ground state solutions. Our method is based on the Pohozˇaev type identity and monotone trick.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant numbers 11361042, 11771198, 11901276, 11961045] and Jiangxi Provincial Natural Science Foundation [20181BAB201003, 20202BAB201001, 20202BAB211004].

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