非线性一阶半正周期边值问题正解的存在性

Existence of Positive Solutions forNonlinear First-Order Semi-PositivePeriodic Boundary Problems

摘要: 本文研究了一类半正周期边值问题正解的存在性，其中λ为正参数，ε是一个正数，a,b∈C(ℝ,[0,∞)) 是1-周期函数且∫₀¹a(t)dt > 0，∫₀¹b(t)dt > 0，f,g∈C([0,∞),[0,∞))，τ(t)是连续1-周期函数。运用上下解方法和拓扑度理论，得到存在常数λ∗ > 0，使得当λ∈(0,λ∗)时，问题(P)存在两个正解。

Abstract: We are concerned with the existence of positive solutions for a class of semi-positive periodic boundary problems where λ is a positive parameter, ε is a positive constant,a,b∈C(ℝ,[0,∞)) is a 1-periodic function, ∫₀¹a(t)dt > 0，∫₀¹b(t)dt > 0. f,g∈C([0,∞),[0,∞))，τ(t) is a continuous 1-periodic function. By using the method of upper and lower solutions and topological degree theory, we show that there exists a constant λ∗ > 0, such that the problem (P) has two positive solutions for λ∈(0,λ∗).