Abstract:
The monotonic iteration method of nontrivial solutions is studied for a nonlinear third-order two-point boundary value problem in which the nonlinear term contains first and second derivatives of unknown function and may change sign.By applying Green function the problem is transformed into an integral equation.By constructing two monotonically iterative sequences and considering the convergence of these sequences,the existence of nonzero fixed points is proved for the associated integral operator.Further,the existence of nontrivial solutions is verified for the third-order two-point boundary value problem.