Bargmann-Type Inequality for Half-Linear Differential Operators. (28th September 2009)

• Record Type: Journal Article
• Authors: Bognár, Gabriella; Došlý, Ondřej
• Other Names: Bohner Martin J. Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-09-28
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/104043
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : We consider the perturbed half-linear Euler differential equation( Φ ( x ′ ) ) ′ + [ γ / t p + c ( t ) ] Φ ( x ) = 0, Φ ( x ) : = | x | p − 2 x, p > 1, with the subcritical coefficientγ < γ p : = ( ( p − 1 ) / p ) p . We establish a Bargmann-type necessary condition for the existence of a nontrivial solution of this equation with at least( n + 1 ) zero points in( 0, ∞ ) .