Ground State Solution for an Autonomous Nonlinear Schrödinger System

Liu, Min; Liu, Jiu

doi:10.1155/2021/1003941

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Introduction and Main Results1

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2022

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“…In addition, there are many results about semiclassical state solutions, sign-changing solutions, normalized solutions and ground state solutions of elliptic systems, see for example, [1,7,8,10,11,15,20,[22][23][24][25][26][27][28][29] and the references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The existence and non-existence of ground state solutions to Schrödinger systems with general potentials

Liu

2022

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In this paper, we first study the existence of ground state solutions for the following Schrödinger systems { − ∆ u + V ∞ u = G u ( u , v ) , x ∈ R N , − ∆ v + V ∞ v = G v ( u , v ) , x ∈ R N , u , v > 0 , u , v ∈ H 1 ( R N ) , where N≥3 and G ∈ C 2 ( ( R + ) 2 , R ) . And then, by using variational method and projections on Nehari-Poho z ̆ aev type manifold, we will prove the nonexistence of ground state solutions for the coupled Schrödinger systems { − ∆ u + V ( x ) u = G u ( u , v ) , x ∈ R N , − ∆ v + V ( x ) v = G v ( u , v ) , x ∈ R N , u , v > 0 , u , v ∈ H 1 ( R N ) .

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