Multiple normalized solutions for ( 2 , q ) -Laplacian equation problems in whole R N

This paper considers the existence of multiple normalized solutions of the following ( 2 , q ) -Laplacian equation: { − Δ u − Δ q u = λ u + h ( ϵ x ) f ( u ) , i n   R N , ∫ R N | u | 2 d x = a 2 , where 2 < q < N , ϵ > 0 , a > 0 and λ ∈ R is a Lagrange multiplier which is unknown, h is...

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Published inElectronic journal of qualitative theory of differential equations no. 48; pp. 1 - 19
Main Authors Chen, Renhua, Wang, Li, Song, Xin
Format Journal Article
LanguageEnglish
Published 2024
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Abstract This paper considers the existence of multiple normalized solutions of the following ( 2 , q ) -Laplacian equation: { − Δ u − Δ q u = λ u + h ( ϵ x ) f ( u ) , i n   R N , ∫ R N | u | 2 d x = a 2 , where 2 < q < N , ϵ > 0 , a > 0 and λ ∈ R is a Lagrange multiplier which is unknown, h is a continuous positive function and f is also continuous satisfying L 2 -subcritical growth. When ϵ is small enough, we show that the number of normalized solutions is at least the number of global maximum points of h by Ekeland's variational principle.
AbstractList This paper considers the existence of multiple normalized solutions of the following ( 2 , q ) -Laplacian equation: { − Δ u − Δ q u = λ u + h ( ϵ x ) f ( u ) , i n   R N , ∫ R N | u | 2 d x = a 2 , where 2 < q < N , ϵ > 0 , a > 0 and λ ∈ R is a Lagrange multiplier which is unknown, h is a continuous positive function and f is also continuous satisfying L 2 -subcritical growth. When ϵ is small enough, we show that the number of normalized solutions is at least the number of global maximum points of h by Ekeland's variational principle.
Author Wang, Li
Chen, Renhua
Song, Xin
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