Eigenvalue criteria for the existence of multiple positive solutions of high-order nonlinear BVPs

• Published in: Nonlinear analysis Vol. 69; no. 1; pp. 295 - 303
• Main Author: Jiang, Weihua
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.07.2008; Elsevier
• Subjects: 34B10; 34B15; [formula omitted]-point boundary value problem; Eigenvalue criteria; Exact sciences and technology; Green’s function; Mathematical analysis; Mathematics; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Ordinary differential equations; Partial differential equations, boundary value problems; Sciences and techniques of general use; 34B15; Green’s function; Eigenvalue criteria; 34B10; m -point boundary value problem; Green's function; Eigenvalue criteria; m-point boundary value problem; Boundary value problem; Existence of solution; Nonlinear analysis; Eigenvalue; 34B10; 34B15; Mathematical model; Green function
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2007.05.020

The existence of multiple positive solutions for the integral equation u ( t ) = ∫ 0 1 g ( t , s ) h ( s ) f ( s , A n − 1 u ( s ) , … , A 1 u ( s ) , u ( s ) ) d s is studied by using eigenvalue criteria. Using these results we obtain new results on the existence of multiple positive solutions for high-order nonlinear differential equations, subject to local and nonlocal boundary conditions.