On the existence of positive solutions for nonlinear two-point boundary-value problems (Q1347684)

For the boundary value problem \[ -x''+ A(t)x= g(t,x),\quad x(0)= x(1)= 0, \] with \(x\in \mathbb{R}^N\), the existence of solutions is studied whose coordinates are nonnegative. The matrix \(A(t)\) is symmetric. The author separately considers the case of potential nonlinearity \(g(t,x)= \nabla_x G(t,x)\) and the case when \(g(t,x)\) satisfies certain inequalities. The proofs employ positive operators and variational methods.