Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We prove the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem (-Δ)α/2u=a1(x)uσ1+a2(x)uσ2, in D limx→z∈∂D(δ(x))1-(α/2)u(x)=0, where 0<α<2, σ1, σ2∈(-1,1), D is a bounded C1,1-domain in ℝn,n≥2, and δ(x) denotes the Euclidian distance from x to the boundary of D.
The nonnegative weight functions a1, a2 are required to satisfy certain hypotheses related to the Karamata class.
We also investigate the global behavior of such solution.
American Psychological Association (APA)
Bachar, Imed& Mâagli, Habib. 2013. Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-461238
Modern Language Association (MLA)
Bachar, Imed& Mâagli, Habib. Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains. Abstract and Applied Analysis No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-461238
American Medical Association (AMA)
Bachar, Imed& Mâagli, Habib. Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-461238
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-461238