Positive solutions for asymptotically 3-linear quasilinear Schrödinger equations
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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].
CitationLi, G., Cheng, B., & Huang, Y. (2020). Positive solutions for asymptotically 3-linear quasilinear Schrödinger equations. Electronic Journal of Differential Equations, 2020(56), pp. 1-17.
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