Fall dormancy (FD) is an important indicator of winter hardiness in alfalfa (Medicago sativa L.), but the relationship between FD and the yield potential of alfalfa varieties with contrasting FD classes has not been determined in the temperate regions with mild winters. This study was conducted with 42 varieties of eight FD classes (2–9) over four consecutive years to determine the relationship of seasonal and annual total dry matter (DM) yields with FD classes. The results showed that all the eight FD varieties survived over the winter without any persistency problems during the four production years. The greatest average DM yield of 24.4 Mg ha−1 yr−1 was achieved with ‘Runner’ (FD2), while the smallest yields were found in ‘Defi’ (FD5). There were no differences in annual DM yields of varieties among FD classes 3 and 5 to 9. Time of cuts affected DM yields (P < 0.01) with the first three cuts accounted for 80% of the total yields. Dry matter yields for some of the dormant, semidormant and nondormant varieties were also the greatest and notable yield differences (P < 0.05) were found among the same FD varieties, whereas overall annual total DM yields were not correlated with FD classes. Our data suggest that FD class should not be used as the main criteria for alfalfa variety improvement and/or introduction of new varieties into temperate regions, and also highlight the importance of early season management to achieve great annual total herbage yields in the temperate regions, such as North Central China.

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We consider poly‐harmonic equations with critical exponents. Under some conditions on the coefficient K(y) in the equations near its critical points, we prove the existence and local uniqueness of solutions with infinitely many bubbles. The local uniqueness result implies that some bubbling solutions preserve the symmetry of the scalar curvature K(y). Moreover, we also show that the conditions imposed are optimal to obtain such results.

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