Existence of Nonnegative Solutions for Semi-Infinity Interval Problems

Using the degree theorem and the nonlinear alternative theorem, the authors turned the boundary value problems into equivalent operator equations and obtained the existence of solutions for the boundary value problems on the finite interval. Combining the property of nonlinear function f(t,y) with a diagonalization argument, the authors studied the singular boundary value problems on the semi-infinite interval. Besides, they provided the sufficient conditions which guarantee the existence of nonnegative solutions for this problem.