Existence of Nontrivial Solutions of p-Laplacian Equation with Sign-Changing Weight Functions. (12th February 2014)

• Record Type: Journal Article
• Authors: Abdeljabbar, Ghanmi
• Other Names: Colorado E. Academic Editor.; Gasinski L. Academic Editor.; Hai D. D. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2014(2014)
• Publication Date: 2014-02-12
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.1155/2014/461965
• Languages: English
• ISSNs: 2090-4657

Abstract

Abstract : This paper shows the existence and multiplicity of nontrivial solutions of the p -Laplacian problem - Δ p u = 1 / σ ( ∂ F ( x, u ) / ∂ u ) + λ a ( x ) | u | q - 2 u for x ∈ Ω with zero Dirichlet boundary conditions, where Ω is a bounded open set in ℝ n, 1 < q < p < σ < p * ( p * = n p / ( n - p ) if p < n, p * = ∞ if p ≥ n ), λ ∈ ℝ ∖ { 0 }, a is a smooth function which may change sign in Ω ̅, , and F ∈ C 1 ( Ω ̅ × ℝ, ℝ ) . The method is based on Nehari results on three submanifolds of the space W 0 1, p ( Ω ) .