Normalized solutions for the p-Laplacian equation with a trapping potential

In this article, we are concerned with normalized solutions for the -Laplacian equation with a trapping potential and -supercritical growth, where or The solutions correspond to critical points of the underlying energy functional subject to the -norm constraint, namely, for given When we show that s...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 12; no. 1; pp. 457 - 472
Main Authors Wang, Chao, Sun, Juntao
Format Journal Article
LanguageEnglish
Published De Gruyter 27.03.2023
Subjects
35J20
35J60
35J92
Laplacian equation
normalized solutions
p-laplacian equation
variational methods
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Summary:In this article, we are concerned with normalized solutions for the -Laplacian equation with a trapping potential and -supercritical growth, where or The solutions correspond to critical points of the underlying energy functional subject to the -norm constraint, namely, for given When we show that such problem has a ground state with positive energy for small enough. When we show that such problem has at least two solutions both with positive energy, which one is a ground state and the other one is a high-energy solution.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2022-0291