摘要: 考察二阶半正 Dirichlet 边值问题
![](https://image.hanspub.org/IMAGE/Edit_0eb4be16-7872-4e5c-9683-7ac2a81606c3.png)
正解的存在性与多解性,其中入为正参数,f∈C([0,∞),[0,∞)),存在∧> 0,使得∈∈[0,∧]。当f 满足
![](https://image.hanspub.org/IMAGE/Edit_1fd61ce3-c4aa-40bb-9b71-08d6c7de548d.png)
时,运用不动点指数理论和上下解方法证明了存在常数λ
∗ > 0,使得当λ>λ
∗时,问题(P) 至少存在两个正解。
Abstract:
In this paper,we are considered with the existence and multiplicity of positive solutions for second-order Dirichlet boundary value problems
![](https://image.hanspub.org/IMAGE/Edit_92e75142-94d1-406f-8346-51789b7d7643.png)
where λ is a positive parameter, f∈C([0,∞),[0,∞)), there exists ∧> 0, such that ∈∈[0,∧]. When f satisfies
![](https://image.hanspub.org/IMAGE/Edit_decd43a8-7c65-41e0-873a-8a1aeed0db7f.png)
, we apply a fixed point index theorem and the method of the upper and lower solutions to prove that there exists λ
∗ > 0 such that the problem (P) has at least two positive solutions for λ>λ
∗.