On Ground States and Compactly Supported Solutions of Elliptic Equations with Non-Lipschitz Nonlinearities

In a bounded domain Ω ⊂ ℝ N , we consider the Dirichlet boundary-value problem for an elliptic equation with a non-Lipschitz nonlinearity of the form Δ u = λ u − u α − 1 u , λ ∈ ℝ , 0 < α < 1 . The problem of the existence of a solution of the ground-state-type with compact support is examined...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 258; no. 1; pp. 110 - 114
Main Author Kholodnov, E. E.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2021
Springer
Springer Nature B.V
Subjects
Boundary value problems
Dirichlet problem
Elliptic functions
Mathematics
Mathematics and Statistics
Nonlinearity
solution with compact support
35J60
35J70
35B44
35B32
non-Lipschitz nonlinearity
35K59
elliptic equation
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-021-05539-4

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Summary:In a bounded domain Ω ⊂ ℝ N , we consider the Dirichlet boundary-value problem for an elliptic equation with a non-Lipschitz nonlinearity of the form Δ u = λ u − u α − 1 u , λ ∈ ℝ , 0 < α < 1 . The problem of the existence of a solution of the ground-state-type with compact support is examined.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05539-4