Existence of three solutions for a first-order problem with nonlinear non-local boundary conditions

Abstract

Conditions for the existence of at least three positive solutions to the nonlinear first-order problem with a nonlinear nonlocal boundary condition given by && y'(t) - p(t)y(t) = \sum_{i=1}^m f_i\big(t,y(t)\big), \quad t\in[0,1], && λy(0) = y(1) + \sum_{j=1}^n Φ_j(τ_j,y(τ_j)), \quad τ_j\in[0,1], are discussed, for sufficiently large $\lambda >1$. The Leggett-Williams fixed point theorem is utilized.

outline, 6 pages