Existence and multiplicity results for some three-point boundary value problems

• Published in: Nonlinear analysis Vol. 66; no. 8; pp. 1686 - 1697
• Main Authors: Khan, Rahmat Ali, Rafique, M.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.04.2007; Elsevier
• Subjects: Exact sciences and technology; Mathematical analysis; Mathematics; Multiple solutions; Ordinary differential equations; Sciences and techniques of general use; Three-point boundary conditions; Topological degree; Upper and lower solutions; Multiple solutions; 34B15; Upper and lower solutions; Three-point boundary conditions; 34B10; Topological degree; primary; 34B18; 34B18,Three-point boundary conditions; Upper and lower solutions; Topological degree; Multiple solutions; Multiple solution; Boundary value problem; Nonlinear analysis; primary 34B10; Boundary condition; Mathematical model
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2006.02.017

Using the method of upper and lower solutions and some degree theory arguments, we establish the existence of at least three solutions of some second-order nonlinear differential equations of the type − x ″ = f ( t , x , x ′ ) , t ∈ I = [ 0 , 1 ] subject to nonlinear three-point boundary conditions x ( 0 ) = 0 , x ′ ( 1 ) = g ( x ( η ) ) , 0 < η ≤ 1 . The growth of f with respect to x ′ is allowed to be quadratic.