Li, GuofaCheng, BitaoHuang, Yisheng2021-09-292021-09-292020-06-04Li, G., Cheng, B., & Huang, Y. (2020). Positive solutions for asymptotically 3-linear quasilinear Schrödinger equations. <i>Electronic Journal of Differential Equations, 2020</i>(56), pp. 1-17.1072-6691https://hdl.handle.net/10877/14563In this article, we study the quasilinear Schrödinger equation -Δu + V(x)u - k/2 [Δ(1 + u2)1/2] u/(1 + u2)1/2 = h(u), x ∈ ℝN, where N ≥ 3, k > 0 is a parameter, V : ℝN → ℝ is a given potential. The nonlinearity h ∈ C(ℝ, ℝ) is asymptotically 3-linear at infinity. We obtain the nonexistence of a least energy solution and the existence of a positive solution, via the Pohožaev manifold and a linking theorem. Our results improve recent results in [4, 22].Text17 pages1 file (.pdf)enAttribution 4.0 InternationalQuasilinear Schrödinger equationsAsymptotically 3-linearPohozaev identityLinking theoremPositive solutionArticle