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Some properties of relatively strong pseudocompactness

Guo-Fang Zhang — 2008

Czechoslovak Mathematical Journal

In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space X and a subspace Y satisfy that Y Int Y ¯ and Y is strongly pseudocompact and metacompact in X , then Y is compact in X . We also give an example to demonstrate that the condition Y Int Y ¯ can not be omitted.

On existence theorems for semilinear equations and applications

Fang ZhangFeng Wang — 2013

Annales Polonici Mathematici

Existence results for semilinear operator equations without the assumption of normal cones are obtained by the properties of a fixed point index for A-proper semilinear operators established by Cremins. As an application, the existence of positive solutions for a second order m-point boundary value problem at resonance is considered.

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