Multiple nonnegative solutions of second-order systems of boundary value problems
The author deals with the existence of at least two nonnegative solutions to a vector boundary value problem of the form \[ x''+\lambda a(t)f(x(t),y(t))=0, \quad y''+\lambda b(t)g(x(t),y(t))=0, \quad 0\leq t\leq 1, \] with the boundary conditions \(x(0)=x(1)=0\) and \(y(0)=y(1)=0.\) The dimensions of the range of the functions \(f\) and \(g\) are not necessary the same. The functions \(a,b\) are diagonal-valued with positive components. The author provides sufficient conditions so that by applying a fixed-point theorem in a cone the existence of at least two nonnegative solutions is guarranteed.
scientific article; zbMATH DE number 1526172