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 in | Electronic journal of qualitative theory of differential equations no. 48; pp. 1 - 19 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
2024
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Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 1417-3875 1417-3875 |
DOI: | 10.14232/ejqtde.2024.1.48 |