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Zbl 1015.34012
Livrea, Roberto
Existence of three solutions for a quasilinear two point boundary value problem. (English)
[J] Arch. Math. 79, No.4, 288-298 (2002). ISSN 0003-889X; ISSN 1420-8938/e

The author investigates the existence of at least three classical solutions to the second-order boundary value problem $$u''(t)+ \lambda h\bigl(u'(t)\bigr)f\bigl(t,u(t)\bigr)=0,\quad u(0)=u(1)=0,$$ where $f:[0,1] \to\bbfR$ and $h:\bbfR \to(0,\infty)$ are two continuous functions and $\lambda$ is a positive parameter. The proof of the main result is based upon a three critical points theorem established by {\it B. Ricceri} [Arch. Math. 75, No. 3, 220-226 (2000; Zbl 0979.35040)].
[Ruyun Ma (Lanzhou)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
49J35 Minimax problems (existence)
58E05 Abstract critical point theory

Keywords: boundary value problem; critical points; minimax problem; solutions; multiplicity

Citations: Zbl 0979.35040

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