Three solutions for a Neumann-type differential inclusion problem involving the p(x)-Laplacian

• Published in: Nonlinear analysis Vol. 70; no. 10; pp. 3755 - 3760
• Main Author: Dai, Guowei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.05.2009; Elsevier
• Subjects: [formula omitted]-Laplacian; Differential inclusion problem; Exact sciences and technology; Mathematical analysis; Mathematics; Ordinary differential equations; Partial differential equations; Sciences and techniques of general use; Three-critical-points theorem; 35J20; 35R70; p ( x ) -Laplacian; Differential inclusion problem; Three-critical-points theorem; 35J70; Neumann problem; p(x)-Laplacian; P laplacian; Nonlinear analysis; Critical point; Differential inclusion; Mathematical model
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2008.07.031

In this paper we consider Neumann-type differential inclusion problems involving the p ( x ) -Laplacian of the type { − div ( | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u ∈ λ ∂ F ( x , u )  in  Ω , ∂ u ∂ γ = 0  on  ∂ Ω . Applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W 0 1 , p ( x ) ( Ω ) .