摘要: 本文研究了二阶非线性微分方程边值问题
正解的存在性及多解性, 其中b是正参数,k > 0,a∈C([0,1],(0,∞)),f,g∈C([0,∞), (0,∞)).在f,g满足适当条件下证得存在一个正数b
∗, 使得当0 < b < b
∗时,(P)至少存在两个正解; 当b=b
∗时,(P)存在一个正解,当b > b
∗时,(P)不存在正解.主要结果的证明基于拓扑度理论和上下解方法。
Abstract:
In this paper, we are concerned with the existence and multiplicity of positive solutions
for second order nonlinear differential equations boundary value problems
where b is a positive parameter,k > 0,a∈C([0,1],(0,∞)),f,g∈C([0,∞), (0,∞)).When f and g satisfy the proper conditions, we prove that there exists a positive number b
∗, such that (P) has zero, exactly one and at least two positive solutions according to b > b
∗,b=b
∗ and 0 < b < b
∗, respectively. The proof of the main results is based on topological theory and the method of upper and lower solutions.