We apply the three-critical-point theorem of Ricceri to prove the existence of at least three solutions of certain two-parameter Dirichlet problems defined on the classical fractal object – the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameter Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti and Rabinowitz and that of Pucci and Serrin. The journal in which the paper appeared is near the top of the SCI list.
COBISS.SI-ID: 15657049
We extend the definition of Bockstein basis $\sigma(G)$ to nilpotent groups $G$. The Bockstein First Theorem says that all compact spaces are Bockstein spaces. Here are the main results of the paper: Theorem 0.1. Let $X$ be a Bockstein space. If $G$ is nilpotent, then $\dim_G(X) \le 1$ if and only if $\sup \{ \dim_H(X)\vert H \in \sigma(G)\} \le 1$. Theorem 0.2. $X$ is a Bockstein space if and only if $\dim_{Z(l)}(X) = \dim_{\hat{Z}(l)}(X)$ for all subsets $l$ of prime numbers. The journal in which the paper appeared is high on the SCI list.
COBISS.SI-ID: 15493977