We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p-...We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p- 1)-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.展开更多
: The genetic variation and clonal diversity of two divergent types (grey-green and yellow-green) of clonal populations of Leymus chinensis Tzvel at 14 loci were compared. Total gene diversity (HT) and the coefficient...: The genetic variation and clonal diversity of two divergent types (grey-green and yellow-green) of clonal populations of Leymus chinensis Tzvel at 14 loci were compared. Total gene diversity (HT) and the coefficient of genetic differentiation (GST) were all higher for the yellow-green type (HT=0.270; GST= 0.186) than for the grey-green type (HT= 0.250; GST= 0.157) of L. chinensis. Rare alleles usually occurred as heterozygotes rather than homozygotes and significant deviations from Hardy-Weinberg equilibrium were found only at a few loci. This indicated that these two types of populations were mainly out-crossing. Clonal diversity, evenness of clones, and mean clone size were not significantly different between the two types. We found that differences between the clone size and genetic variation of the yellow-green type of populations occurred with different climate and habitat population groups. However, for the grey-green type of populations, these genetic variations decreased under conditions of different climate and habitat population groups.展开更多
基金Supported by the NNSF of China(11101145)Supported by the NSF of Henan Province(102102210216)
文摘We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p- 1)-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.
文摘: The genetic variation and clonal diversity of two divergent types (grey-green and yellow-green) of clonal populations of Leymus chinensis Tzvel at 14 loci were compared. Total gene diversity (HT) and the coefficient of genetic differentiation (GST) were all higher for the yellow-green type (HT=0.270; GST= 0.186) than for the grey-green type (HT= 0.250; GST= 0.157) of L. chinensis. Rare alleles usually occurred as heterozygotes rather than homozygotes and significant deviations from Hardy-Weinberg equilibrium were found only at a few loci. This indicated that these two types of populations were mainly out-crossing. Clonal diversity, evenness of clones, and mean clone size were not significantly different between the two types. We found that differences between the clone size and genetic variation of the yellow-green type of populations occurred with different climate and habitat population groups. However, for the grey-green type of populations, these genetic variations decreased under conditions of different climate and habitat population groups.
