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Multiplicity of Solutions for a Class of Elliptic Problem of p-Laplacian Type with a p-Gradient Term
Joint Authors
Chaouai, Zakariya
Maatouk, Soufiane
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-02-05
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We consider the following problem: -Δpu=c(x)|u|q-1u+μ|∇u|p+h(x) in Ω, u=0 on ∂Ω, where Ω is a bounded set in RN (N≥3) with a smooth boundary, 1
0, μ∈R⁎, and c and h belong to Lk(Ω) for some k>N/p.
In this paper, we assume that c≩0 a.e.
in Ω and h without sign condition and then we prove the existence of at least two bounded solutions under the condition that ck and hk are suitably small.
For this purpose, we use the Mountain Pass theorem, on an equivalent problem to (P) with variational structure.
Here, the main difficulty is that the nonlinearity term considered does not satisfy Ambrosetti and Rabinowitz condition.
The key idea is to replace the former condition by the nonquadraticity condition at infinity.
American Psychological Association (APA)
Chaouai, Zakariya& Maatouk, Soufiane. 2019. Multiplicity of Solutions for a Class of Elliptic Problem of p-Laplacian Type with a p-Gradient Term. International Journal of Mathematics and Mathematical Sciences،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1166381
Modern Language Association (MLA)
Chaouai, Zakariya& Maatouk, Soufiane. Multiplicity of Solutions for a Class of Elliptic Problem of p-Laplacian Type with a p-Gradient Term. International Journal of Mathematics and Mathematical Sciences No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1166381
American Medical Association (AMA)
Chaouai, Zakariya& Maatouk, Soufiane. Multiplicity of Solutions for a Class of Elliptic Problem of p-Laplacian Type with a p-Gradient Term. International Journal of Mathematics and Mathematical Sciences. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1166381
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1166381