【摘要】 把边值问题转化成相应的算子方程,运用拓扑理论、非线性更替定理得出:如果有限区间上带参数λ(其中λ∈[0,1))的边值问题的解一致有界,那么当λ=1时该问题也存在解.通过考察非线性项f(t,y)的性质,结合Lebesgue控制收敛定理、对角化原理和Arzela-Ascoil定理研究了奇异半无穷区间问题,并给出半无穷区间边值问题非负解存在的充分条件.更多还原

【Abstract】 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.更多还原