SECOND ORDER PROBLEM WITH ALP CONDITION AND UNBOUNDED NONLINEARITIES

摘要

The nonlinear second order ordinary differential equation u"(x) + m~2 u(x) + g(x, u(x)) = f(x), x ∈ [0,π], u(0)=u(π) = 0 is investigated in this article. We suppose that the nonlinearity g is unbounded and satisfies an ALP type condition. We prove the existence result to this problem using a saddle point theorem.