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Zbl 1066.34019
Bai, Zhanbing; Ge, Weigao
Existence of three positive solutions for some second-order boundary value problems.
(English)
[J] Comput. Math. Appl. 48, No. 5-6, 699-707 (2004). ISSN 0898-1221

Summary: A new fixed-point theorem of functional type in a cone is established. Using this fixed-point theorem and imposing growth conditions on the nonlinearity, the existence of three positive solutions for the boundary value problem $$x''(t)+ f(t, x(t), x'(t))= 0\quad 0< t< 1,\quad x(0)= x(1)= 0,$$ is obtained. Here, $f: [0,1]\times [0,\infty)\times\bbfR\to[0,\infty)$ is continuous. Finally, an example is given to illustrate the importance of results obtained.
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: Fixed-point theorem; Boundary value problem; Positive solution

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