Existence of Multiple Solutions for Second Order Boundary Value Problems
By J. Henderson, H. Thompson. 2000
103 citations recorded by the source corpus.
We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/9352cab1c433fb14e7878de7d6ecefe1fc7d9a7c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Diego Averna
- Gabriele Bonanno
- Weigao Ge
- Hairong Lian
- Huihui Pang
- Pasquale Candito
- Giuseppina D'Aguì
- Antonia Chinnì
In Computational Theory and Mathematics
- Diego Averna
- Weigao Ge
- Gabriele Bonanno
- Pasquale Candito
- Giuseppina D'Aguì
- Antonia Chinnì
- Vicentiu D. Rădulescu
- Giovanni Molica Bisci
Citations in the corpus
- Upper and lower solutions method and a fractional differential equation boundary value problem. (2009, unknown): “The lower and upper solutions method plays very important role in investigating the existence of solutions to ordinary differential equation problems of integer orders, for example, [9] [ 11 ].”
- Triple positive solutions for boundary value problems on infinite intervals (2007, background): “Especially, the existence of triple positive solutions attracts much attention [2–8].”
- A three critical points theorem and its applications to the ordinary Dirichlet problem (2003, methodology): “and the authors give an example (see Remark 7 of [ 10 ]) where (HT) fails and the problem has only the trivial solution.”