Positive Solutions for Integral Boundary Value Problem with ϕ-Laplacian Operator. (23rd February 2011)

• Record Type: Journal Article
• Authors: Ding, Yonghong
• Other Names: Lieberman Gary Academic Editor.
• Is Part Of: Boundary value problems. Volume 2011(2011)
• Publication Date: 2011-02-23
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2011/827510
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We consider the existence, multiplicity of positive solutions for the integral boundary value problem withϕ -Laplacian( ϕ ( u ′ ( t ) ) ) ′ + f ( t, u ( t ), u ′ ( t ) ) = 0, t ∈ [ 0, 1 ], u ( 0 ) = ∫ 0 1 u ( r ) g ( r ) d r, u ( 1 ) = ∫ 0 1 u ( r ) h ( r ) d r, whereϕ is an odd, increasing homeomorphism fromℝ ontoℝ . We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems. The interesting point is that the nonlinear termf is involved with the first-order derivative explicitly.