A three critical points theorem and its applications to the ordinary Dirichlet problem

Diego Averna, Gabriele Bonanno

Abstract


The aim of this paper is twofold. On one hand we establish a three
critical points theorem for functionals depending on a real parameter
$\lambda \in \Lambda$, which is different from the one proved by B. Ricceri
in [Arch. Math. {\bf 75} (2000), 220-226]
and gives an
estimate of where $\Lambda$ can be located. On the other hand, as an
application of the previous result, we prove an existence theorem of three
classical solutions for a two-point boundary value problem which is
independent from the one by J. Henderson and H. B. Thompson
[J. Differential Equations {\bf 166} (2000), 443-454].
Specifically, an example is given where the key assumption of
[J. Differential Equations {\bf 166} (2000), 443-454] fails. Nevertheless, the existence of three
solutions can still be deduced using our theorem.

Keywords


Critical points; three solutions; two point boundary value problem

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