Ground state solution for a class of Kirchhoff-type equation with general convolution nonlinearity

In this paper, we consider the following class of Kirchhoff-type equation - ( a + b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = ( I α ∗ F ( u ) ) f ( u ) , in R N , u ∈ H 1 ( R N ) , where a > 0 , b ≥ 0 , N ≥ 3 , α ∈ ( N - 2 , N ) , V : R N → R is a potential function and I α is a Riesz potential of...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 73; no. 2
Main Authors Zhou, Li, Zhu, Chuanxi
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2022
Springer Nature B.V
Subjects
Engineering
Ground state
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Variational methods
Kirchhoff equation
35A15
35J60
Nehari manifold
Pohozaev identity
35J35
Ground state solutions
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Summary:In this paper, we consider the following class of Kirchhoff-type equation - ( a + b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = ( I α ∗ F ( u ) ) f ( u ) , in R N , u ∈ H 1 ( R N ) , where a > 0 , b ≥ 0 , N ≥ 3 , α ∈ ( N - 2 , N ) , V : R N → R is a potential function and I α is a Riesz potential of order α ∈ ( N - 2 , N ) . Under certain assumptions on V ( x ) and f ( u ), we prove that the equation has ground state solutions by variational methods.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01712-0