Fractional p‐Laplacian problem with indefinite weight in RN: Eigenvalues and existence

In this paper, we first study the fractional p‐Laplacian eigenvalue problem with indefinite weight (−Δp)su=λg(x)|u|p−2uinRN and prove that the problem exists a sequence of eigenvalues that converges to infinity and that the first eigenvalue is simple. Based on these results, we then consider the exi...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-02, Vol.44 (3), p.2585-2599
Main Authors: Cui, Na, Sun, Hong‐Rui
Format: Article
Language:English
Subjects:
eigenvalue problem
Eigenvalues
fractional p‐Laplacian
indefinite potential
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Summary:In this paper, we first study the fractional p‐Laplacian eigenvalue problem with indefinite weight (−Δp)su=λg(x)|u|p−2uinRN and prove that the problem exists a sequence of eigenvalues that converges to infinity and that the first eigenvalue is simple. Based on these results, we then consider the existence of infinitely many solutions for a class of indefinite weight problem with concave and convex nonlinearities.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6323