Nodal solutions for logarithmic weighted N-laplacian problem with exponential nonlinearities

In this article, we study the following problem - d i v ( ω ( x ) | ∇ u | N - 2 ∇ u ) = λ f ( x , u ) in B , u = 0 on ∂ B , where B is the unit ball in R N , N ≥ 2 and w ( x ) a singular weight of logarithm type. The reaction source f ( x ,  u ) is a radial function with respect to x and is subcriti...

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Bibliographic Details
Published in:Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche 2024-02, Vol.70 (1), p.63-88
Main Authors: Dridi, Brahim, Jaidane, Rached
Format: Article
Language:English
Subjects:
Algebraic Geometry
Analysis
Geometry
History of Mathematical Sciences
Logarithms
Mathematics
Mathematics and Statistics
Numerical Analysis
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Summary:In this article, we study the following problem - d i v ( ω ( x ) | ∇ u | N - 2 ∇ u ) = λ f ( x , u ) in B , u = 0 on ∂ B , where B is the unit ball in R N , N ≥ 2 and w ( x ) a singular weight of logarithm type. The reaction source f ( x ,  u ) is a radial function with respect to x and is subcritical or critical with respect to a maximal growth of exponential type. By using the constrained minimization in Nehari set coupled with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions.
ISSN:0430-3202
1827-1510
DOI:10.1007/s11565-023-00457-6