Existence of Multiple Solutions for Second Order Boundary Value Problems
β Scribed by Johnny Henderson; H.B. Thompson
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 128 KB
- Volume
- 166
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
We establish the existence of at least three positive solutions to the second-order three-point boundary value problem, u + f t u = 0 u 0 = 0 Ξ±u Ξ· = u 1 , where Ξ· 0 < Ξ· < 1 0 < Ξ± < 1/Ξ·, and f 0 1 Γ 0 β β 0 β is continuous. We accomplish this by making growth assumptions on f which can apply to many
Existence results for the second-order three-point boundary value problem Ε½ . Ε½ . Ε½ . Ε½ . Ε½ . xΠ s f t, x, xΠ , x 0 s A, x y x 1 s y 1 B, 0 --1, are presented. Our analysis is based on a Nonlinear Alternative of Leray-Schauder.
with the same boundary conditions. Under various assumptions on f , a, and Ξ» we establish intervals of the parameter Ξ» which yield the existence of a positive solution of the eigenvalue problem. By placing certain restrictions on the nonlinearity, we prove the existence of at least one, at least two