On The Solution n-Dimensional of the Composite ♢k Operator and ♢Bk Operator. (17th October 2012)

• Record Type: Journal Article
• Authors: Satsanit, Wanchak
• Other Names: Lu C. Academic Editor.; Mishuris G. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-10-17
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/952191
• Languages: English
• ISSNs: 2090-5564

Abstract

Abstract : Firstly, we study the solution of the equation ♢ k ♢ B k u ( x ) = f ( x ), where ♢ k ♢ B k is the composite of the diamond operator and Bessel diamond operator. Finally, we study of the nonlinear equation ♢ k ♢ B k u ( x ) = f ( x, ∆ k - 1 □ k ♢ B k ) . It was found that the existence of the solution u ( x ) of such an equation depends on the condition of f and ∆ k - 1 □ k ♢ B k u ( x ) . Moreover, such equation u ( x ) is related to the elastic wave equation.