A three critical points theorem and its applications to the ordinary Dirichlet problem
Keywords
Critical points, three solutions, two point boundary value problemAbstract
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.Downloads
Published
2003-09-01
How to Cite
1.
AVERNA, Diego and BONANNO, Gabriele. A three critical points theorem and its applications to the ordinary Dirichlet problem. Topological Methods in Nonlinear Analysis. Online. 1 September 2003. Vol. 22, no. 1, pp. 93 - 103. [Accessed 29 March 2024].
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