A three critical points theorem and its applications to the ordinary Dirichlet problem
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Critical points, three solutions, two point boundary value problemAbstrakt
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.Pobrania
Opublikowane
2003-09-01
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AVERNA, Diego & BONANNO, Gabriele. A three critical points theorem and its applications to the ordinary Dirichlet problem. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2003, T. 22, nr 1, s. 93–103. [udostępniono 22.7.2024].
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