Existence of ground state solutions to the nonlinear kirchho-type equations with potentials

Norihisa Ikoma

doi:10.3934/dcds.2015.35.943

Existence of ground state solutions to the nonlinear kirchho-type equations with potentials

Norihisa Ikoma

研究成果: Article › 査読

30 被引用数 (Scopus)

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In this paper, we study the existence of ground state solutions to the nonlinear Kirchho- type equations -m(||∇_u||² L²(R^N)) Δu + V (x)u = |u|^p-1u in R^N; u ∈ H¹(R^N); N ≥ 1 where 1 < p < ∞ when N = 1; 2, 1 < p < (N + 2)=(N - 2) when N ≥ 3, m : [0,∞) → (0,∞) is a continuous function and V : R^N → R a smooth function. Under suitable conditions on m(s) and V , it is shown that a ground state solution to the above equation exists.

本文言語	English
ページ（範囲）	943-966
ページ数	24
ジャーナル	Discrete and Continuous Dynamical Systems- Series A
巻	35
号	3
DOI	https://doi.org/10.3934/dcds.2015.35.943
出版ステータス	Published - 2015 3月 1
外部発表	はい

ASJC Scopus subject areas

分析
離散数学と組合せ数学
応用数学

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abstract = "In this paper, we study the existence of ground state solutions to the nonlinear Kirchho- type equations -m(||∇u||2 L2(RN)) Δu + V (x)u = |u|p-1u in RN; u ∈ H1(RN); N ≥ 1 where 1 < p < ∞ when N = 1; 2, 1 < p < (N + 2)=(N - 2) when N ≥ 3, m : [0,∞) → (0,∞) is a continuous function and V : RN → R a smooth function. Under suitable conditions on m(s) and V , it is shown that a ground state solution to the above equation exists.",

keywords = "Ground state solutions, Kirchho- type equations, Monotonicity trick, The Pohozaev identity, Variational methods",

author = "Norihisa Ikoma",

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AB - In this paper, we study the existence of ground state solutions to the nonlinear Kirchho- type equations -m(||∇u||2 L2(RN)) Δu + V (x)u = |u|p-1u in RN; u ∈ H1(RN); N ≥ 1 where 1 < p < ∞ when N = 1; 2, 1 < p < (N + 2)=(N - 2) when N ≥ 3, m : [0,∞) → (0,∞) is a continuous function and V : RN → R a smooth function. Under suitable conditions on m(s) and V , it is shown that a ground state solution to the above equation exists.

KW - Ground state solutions

KW - Kirchho- type equations

KW - Monotonicity trick

KW - The Pohozaev identity

KW - Variational methods

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Existence of ground state solutions to the nonlinear kirchho-type equations with potentials

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