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

Research output: Contribution to journalArticle

13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)943-966
Number of pages24
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume35
Issue number3
DOIs
Publication statusPublished - 2015 Jan 1
Externally publishedYes

Fingerprint

Ground State Solution
Ground state
Smooth function
Continuous Function

Keywords

  • Ground state solutions
  • Kirchho- type equations
  • Monotonicity trick
  • The Pohozaev identity
  • Variational methods

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

@article{783e381bc5314396b54266f8c365295e,
title = "Existence of ground state solutions to the nonlinear kirchho-type equations with potentials",
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",
year = "2015",
month = "1",
day = "1",
doi = "10.3934/dcds.2015.35.943",
language = "English",
volume = "35",
pages = "943--966",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "3",

}

TY - JOUR

T1 - Existence of ground state solutions to the nonlinear kirchho-type equations with potentials

AU - Ikoma, Norihisa

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84908223514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908223514&partnerID=8YFLogxK

U2 - 10.3934/dcds.2015.35.943

DO - 10.3934/dcds.2015.35.943

M3 - Article

VL - 35

SP - 943

EP - 966

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 3

ER -