Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞. (14th January 2016)

• Record Type: Journal Article
• Authors: Shen, Wenguo
• Other Names: Bonanno Gabriele Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2016(2016)
• Publication Date: 2016-01-14
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2016/2386287
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We study the existence of nodal solutions for the following problem:- x ″ = α x + + β x - + r a ( t ) f ( x ), 0 < t < 1, x ( 0 ) = x ( 1 ) = 0, wherer ≠ 0 is a parameter, a ( t ) ∈ C ( [ 0, 1 ], ( 0, ∞ ) ) witha ( t ) ≢ 0 on any subinterval of[ 0, 1 ], x + = m a x { x, 0 }, x - = - m i n { x, 0 }, andα, β ∈ C [ 0, 1 ] ;f ∈ C ( R, R ), s f ( s ) > 0 fors ≠ 0, andf 0, f ∞ ∉ ( 0, ∞ ), wheref 0 = l i m | s | → 0 f ( s ) / s andf ∞ = l i m | s | → + ∞ f ( s ) / s . We use bifurcation techniques to prove our main results.