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Existence of three solutions for a quasilinear two point boundary value problem. (English) Zbl 1015.34012

The author investigates the existence of at least three classical solutions to the second-order boundary value problem

u '' (t)+λhu ' (t)ft , u ( t )=0,u(0)=u(1)=0,

where f:[0,1] and h:(0,) are two continuous functions and λ is a positive parameter. The proof of the main result is based upon a three critical points theorem established by B. Ricceri [Arch. Math. 75, No. 3, 220-226 (2000; Zbl 0979.35040)].

MSC:
34B15Nonlinear boundary value problems for ODE
49J35Minimax problems (existence)
58E05Abstract critical point theory