A sequence of vectors {f1, f2, f3, . . . } in a separable Hilbert space H is said to be a Schauder basis for H if every element f ∈ H has a unique norm-convergent expansion f = ∑ cnfn. If, in addition, there exist positive constants A and B such that A ∑ |cn| ≤ ∥∥∥∑ cnfn∥∥∥2 ≤ B∑ |cn|, then we call {f1, f2, f3, . . . } a Riesz basis. In the first half of this paper, we show that every Schauder ...

The main object of this paper is to investigate the existence solutions for a self-adjoint coupled system nonlinear second-order ordinary differential equations equipped with nonlocal multi-point boundary conditions on an arbitrary domain. We apply Leray–Schauder alternative, Schauder fixed point theorem and Banach contraction mapping principle in order derive results, which are then well-illus...