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