Positive solutions for asymptotically 3-linear quasilinear Schrödinger equations
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Date
2020-06-04
Authors
Li, Guofa
Cheng, Bitao
Huang, Yisheng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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].
Description
Keywords
Quasilinear Schrödinger equations, Asymptotically 3-linear, Pohozaev identity, Linking theorem, Positive solution
Citation
Li, 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.
Rights
Attribution 4.0 International