Nonexistence of stable solutions for quasilinear Schrödinger equation

Lijuan Chen,Caisheng Chen,Hongwei Yang,Hongxue Song

Boundary Value Problems（2018）

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摘要

In this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1 -Δ u- [Δ(1+u^2)^1/2] u/2(1+u^2)^1/2=h(x) | u | ^q-1u, x∈ R^N, where N≥3 , q≥5/2 and the function h(x) is continuous and positive in R^N . Under suitable assumptions on h(x) and q , we prove that Eq. ( 0.1 ) has no nonnegative and stable solutions.

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关键词

Nonexistence of solution,Quasilinear Schrödinger equation,Stable solution

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