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Multiplicity Results for the px-Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition
Joint Authors
Kratou, M.
Alsadhan, S.
Saudi, K.
Source
International Journal of Differential Equations
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-07
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We investigate the singular Neumann problem involving the p(x)-Laplace operator: Pλ{-Δpxu+|u|px-2u =1/uδx+fx,u, in Ω; u>0, in Ω; ∇upx-2∂u/∂ν=λuqx, on ∂Ω}, where Ω⊂RNN≥2 is a bounded domain with C2 boundary, λ is a positive parameter, and px,qx,δx, and fx,u are assumed to satisfy assumptions (H0)–(H5) in the Introduction.
Using some variational techniques, we show the existence of a number Λ∈0,∞ such that problem Pλ has two solutions for λ∈0,Λ, one solution for λ=Λ, and no solutions for λ>Λ.
American Psychological Association (APA)
Saudi, K.& Kratou, M.& Alsadhan, S.. 2016. Multiplicity Results for the px-Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition. International Journal of Differential Equations،Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1105689
Modern Language Association (MLA)
Saudi, K.…[et al.]. Multiplicity Results for the px-Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition. International Journal of Differential Equations No. 2016 (2016), pp.1-14.
https://search.emarefa.net/detail/BIM-1105689
American Medical Association (AMA)
Saudi, K.& Kratou, M.& Alsadhan, S.. Multiplicity Results for the px-Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition. International Journal of Differential Equations. 2016. Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1105689
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1105689