In this paper, by using Krasnoselskii's Fixed Point Theorem in a cone, we study the existence of positive solutions for the second-order three-point boundary value problem where 0 < ฮฑ, ฮท < 1 and f is allowed to change sign. We also give some examples to illustrate our results.
Positive solution for three-point boundary value problems with sign changing nonlinearities
โ Scribed by Jingli Ren; Weigao Ge
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 326 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0893-9659
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โฆ Synopsis
By constructing available operators, some new existence theorems of positive solutions are obtained for a class of three-point boundary value problems u"+Ah(t)f(t,u)=O, 0<t<l, ~(0) -Z~'(0) = 0, u(1) = ~(~), where f is allowed to change sign, ~ C (0,1). The associated Green's function for the above problem is also given. (~) 2004 Elsevier Ltd. All rights reserved.
๐ SIMILAR VOLUMES
For the 2nth-order boundary value problem c~y (2i) (0) -fliy (2i+1) (0) = a~y (2i) (1) +/3~y (2i+1) (1) = 0, O 1, growth conditions are imposed on f which yield the existence of at least two symmetric positive solutions by using the fixed-point theorem in double cones.
By a new approach, we present a new existence result of positive solutions to the following Dirichlet boundary value problem, It is remarkable that the result of this paper is not obtained by employing the fixed-point theorems in cone and the method of the lower and upper functions. Our nonlinearit