Solvability of multi-point boundary value problem at resonance (III)

• Published in: Applied mathematics and computation Vol. 129; no. 1; pp. 119 - 143
• Main Authors: Liu, Bing, Yu, Jianshe
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.06.2002; Elsevier
• Subjects: Boundary value problem; Coincidence degree theory; Exact sciences and technology; Mathematical analysis; Mathematics; Ordinary differential equations; Resonance; Sciences and techniques of general use; 34B15; Resonance; Boundary value problem; Coincidence degree theory; 34B10; Second order equation; Kernel function; Differential equation; Isomorphism; Multiple point boundary value problem; Equation system

In this paper, we consider the following second-order ordinary differential equation (E) x″=f(t,x(t),x ′(t))+e(t), t∈(0,1), subject to one of the following boundary value conditions: (B1) x(0)= ∑ i=1 m−2α ix(ξ i), x(1)=βx(η), (B2) x(0)= ∑ i=1 m−2α ix(ξ i), x ′(1)=βx ′(η), (B3) x ′(0)= ∑ i=1 m−2α ix...