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Zbl 1009.34019
Bonannao, G.
Existence of three solutions for a two point boundary value problem. (English)
[J] Appl. Math. Lett. 13, No.5, 53-57 (2000). ISSN 0893-9659

From the introduction: The autonomous ordinary Dirichlet problem $$u''+ \lambda f(u)= 0,\quad u(0)= u(1)= 0,\tag 1$$ is considered, where $\lambda$ is a positive parameter and $f: \bbfR\to\bbfR$ is a continuous function.\par Under a completely novel assumption on the function $\xi\to \int^\xi_ 0 f(t) dt$, the existence of an open interval $\Lambda\subseteq[0,+\infty[$ is proved such that, for every $\lambda\in \Lambda$, problem (1) has at least three classical solutions.

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
47J30 Variational methods
58E05 Abstract critical point theory

Keywords: autonomous ordinary Dirichlet problem; classical solutions

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