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Zbl 0980.34015
Candito, Pasquale
Existence of three solutions for a nonautonomous two point boundary value problem. (English)
[J] J. Math. Anal. Appl. 252, No.2, 532-537 (2000). ISSN 0022-247X

Here, the author considers the two-point boundary value problem $$u''+\lambda f(t,u)= 0,\quad u(a)= u(b)= 0,\tag 1$$ where $f:[a, b]\times \bbfR\to \bbfR$ is a continuous function. Under some assumptions with respect to $f(t,u)$ there exist an open interval $\Lambda\subseteq ]0,+\infty[$ and a positive real number $q$ such that, for each $\lambda\in\Lambda$, the problem (1) admits at least three solutions belonging to $C^2([a, b])$, whose norms in $W^{1,2}_0([a, b])$ are less than $q$.
[Anatolij Ivan Kolosov (Khar'kov)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34B24 Sturm-Liouville theory

Keywords: nonlinear eigenvalue problem; Sobolev space; two-point boundary value problem; solutions

Cited in: Zbl 1019.34017

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