Semiclassical Solutions for a Kind of Coupled Schrödinger Equations

Jinmei Fan, Yi-rong Jiang and Qiongfen Zhang

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

Abstract: In this paper, we are concerned with the following coupled Schrödinger equations −λ2Δu+a1xu=cxv+a2xup−2u+a3xu2∗−2u,x∈ℝN,−λ2Δv+b1xv=cxu+b2xvp−2v+b3xv2∗−2v,x∈ℝN, where 2 0 is a parameter; and a1, a2, a3, b1, b2, b3, c ∈ C(ℝN, ℝ) and u, v ∈ H1(ℝN). Under some suitable conditions that a10=infa1=0 or b10=infb1=0 and |c(x)|2 ≤ ϑa1(x)b1(x) with ϑ ∈ (0, 1), the above coupled Schrödinger system possesses nontrivial solutions if λ ∈ (0, λ0), where λ0 is related to a1, a2, a3, b1, b2, b3, and N.

Date: 2020
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https://doi.org/10.1155/2020/4378691

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:4378691

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