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In this paper we prove the following assertions:where Ω 1 ∩ Ω 2 is bounded, and let α i = α(Ω i ) be the index of J in Ω i for i = 0, 1, 2. J satisfies the (P S)α 0 -condition if and only if the inequality α 0 < min{α 1 , α 2 } holds; (3) the union of a solvable domain and an unsolvable domain may be solvable and the union of two unsolvable domains may be solvable.

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Social housing projects often face the “not-in-my-back-yard” (NIMBY) backlash from the local community who oppose and reject their construction. Considering the prevalence of NIMBY, this study examines the factors that influence the attitude of the public towards social housing construction under high home ownership rates. We conduct an ordered logistic regression analysis by using 14,275 responses from the 2015 Residential Status Survey in Taiwan. The results show some interesting findings. First, home ownership and families with a child under 18 are two of the most influential variables that have significantly negative influences on the approval of social housing construction. Renters and people with physical and mental disabilities are however more supportive of social housing. Secondly, residents in buildings with high development intensity are very supportive of the construction of social housing. Thirdly, satisfaction with neighborhood environment has a positive impact on social housing approval. Finally, residents who live in dense cities tend to support the construction of social housing. However, residents who live in satellite cities of a metropolitan region are less supportive. The results of this study reveal a regional difference in the approval of residents for social housing construction.