In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-comp...In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem展开更多
Pollen diversity offers abundant clues into the floristic diversity and history of vegetation change. Few palynological studies investigated modem pollen diversity or the past floristic diversity on the Tibetan Plate...Pollen diversity offers abundant clues into the floristic diversity and history of vegetation change. Few palynological studies investigated modem pollen diversity or the past floristic diversity on the Tibetan Plateau （TP）. Based on modem pollen assemblages from 37 topsoils and 63 surface lake sediments in the Nam Co catchment on the central TP, this study quantitatively explored spatial distribution of modem pollen diversity using Shannon-Wiener index （H） and palynological richness （E（Tn）, n=600）. Pollen diversity indices showed spatial variability among vegetation types, reflecting the differences in terrestrial floristic diversity in the lake catchment. Their values were high in the southeastern region of the lake catchment which is covered by alpine steppe, while values were low for alpine meadow and marsh meadow. The pollen diversity in lacustrine pollen assemblage could be an effective proxy to document past floristic diversity. The past floristic diversity in the lake catchment, recovered from a fossil pollen record ofNMLC-1, showed a long-term change of ascending overlaid by several rapid diversity changes during the last 8400 years due to the downward shift of altitudinal vegetation belt driven by a general climatic cooling. The results imply that under the environmental challenge of climate warming and vegetation degradation, alpine vegetation restoration in the Nam Co catchment and the central TP should pay attention to altitudinal vegetation belt and zonal vegetation of alpine steppe, and use the long-term change of floristic diversity as a historical analogue.展开更多
文摘In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem
基金supported by the National Natural Science Foundation of China(Grant Nos.41471169,41690113,41271226,41571189&41330105)
文摘Pollen diversity offers abundant clues into the floristic diversity and history of vegetation change. Few palynological studies investigated modem pollen diversity or the past floristic diversity on the Tibetan Plateau （TP）. Based on modem pollen assemblages from 37 topsoils and 63 surface lake sediments in the Nam Co catchment on the central TP, this study quantitatively explored spatial distribution of modem pollen diversity using Shannon-Wiener index （H） and palynological richness （E（Tn）, n=600）. Pollen diversity indices showed spatial variability among vegetation types, reflecting the differences in terrestrial floristic diversity in the lake catchment. Their values were high in the southeastern region of the lake catchment which is covered by alpine steppe, while values were low for alpine meadow and marsh meadow. The pollen diversity in lacustrine pollen assemblage could be an effective proxy to document past floristic diversity. The past floristic diversity in the lake catchment, recovered from a fossil pollen record ofNMLC-1, showed a long-term change of ascending overlaid by several rapid diversity changes during the last 8400 years due to the downward shift of altitudinal vegetation belt driven by a general climatic cooling. The results imply that under the environmental challenge of climate warming and vegetation degradation, alpine vegetation restoration in the Nam Co catchment and the central TP should pay attention to altitudinal vegetation belt and zonal vegetation of alpine steppe, and use the long-term change of floristic diversity as a historical analogue.
