The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray-Schauder type and on a fixed
Multiple positive solutions for singular problems with mixed boundary data and derivative dependence
✍ Scribed by Baoqiang Yan; Donal O’Regan; Ravi P. Agarwal
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 409 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0895-7177
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For 1 < k < n-1, we study the existence of multiple positive solutions to the singular (k, n -k) conjugate boundary value problem We show that there are at least two positive solutions if f(t, y) is superlinear at c~ and singular at u = 0, t = 0, and t = 1. The arguments involve only positivity pro
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This paper considers a singular m-point dynamic eigenvalue problem on time scales T: We allow f (t, w) to be singular at w = 0 and t = 0. By constructing the Green's function and studying its positivity, eigenvalue intervals in which there exist positive solutions of the above problem are obtained