Combined effects in planar quasilinear Schrödinger equations with superlinear reaction

Article type: Research Article

Authors: Zhang, Ning | Tang, Xianhua | Chen, Sitong^{; *}

Affiliations: School of Mathematics and StatiProof is already open in a different tab. You will be redirected.stics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P.R. China

Correspondence: [*] Corresponding author. E-mail: mathsitongchen@mail.csu.edu.cn.

Abstract: In this paper, we prove the existence of nontrivial solutions for the following planar quasilinear Schrödinger equation: −Δu+V(x)u−Δ(u2)u=g(u),x∈R2, where V∈C(R2,[0,∞)) and g∈C(R,R) is of subcritical exponential growth satisfying some mild conditions. In particular, by means of the Trudinger–Moser inequality, we give a different method from the one of the polynomial growth nonlinearities to prove the Brézis–Lieb split property when f has subcritical exponential growth. Our result extends and complements the one of Chen–Rădulescu–Tang–Zhang (Rev. Mat. Iberoam. 36 (2020) 1549–1570) dealing with the higher dimensions N⩾3 to the dimension N=2.

Keywords: Quasilinear Schrödinger equation, nontrivial solution, exponential growth

DOI: 10.3233/ASY-221785

Journal: Asymptotic Analysis, vol. 132, no. 1-2, pp. 61-82, 2023