Multiple positive solutions for m -point boundary-value problems with a one-dimensional p -Laplacian

• Published in: Nonlinear analysis Vol. 68; no. 8; pp. 2269 - 2279
• Main Authors: Feng, Hanying, Ge, Weigao, Jiang, Ming
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.04.2008; Elsevier
• Subjects: 34B10; 34B15; Boundary value problems; Exact sciences and technology; Fixed point theorem; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Multiple positive solutions; Numerical analysis; Numerical analysis. Scientific computation; One-dimensional [formula omitted]-Laplacian; Partial differential equations, boundary value problems; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; 34B15; Boundary value problems; Fixed point theorem; One-dimensional p -Laplacian; 34B10; Multiple positive solutions; P laplacian; Boundary value problem; Boundary value problems; Multiple positive solutions; Fixed point theorem; One-dimensional p-Laplacian; Nonlinear analysis; Positive solution; 34B10; 34B15; Mathematical model
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2007.01.052

In this paper, we consider the multipoint boundary- value problem for the one-dimensional p -Laplacian ( ϕ p ( u ′ ) ) ′ + q ( t ) f ( t , u ) = 0 , t ∈ ( 0 , 1 ) , subject to the boundary conditions: u ( 0 ) = ∑ i = 1 m − 2 a i u ( ξ i ) , u ( 1 ) = ∑ i = 1 m − 2 b i u ( ξ i ) , where ϕ p ( s ) = | s | p − 2 s . By using a fixed point theorem in a cone, we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem.