The article proved the existence of H<sup>1</sup> （R） ∩ L<sup>∞</sup> （R<sup>n</sup>） at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-（ij）(a<...The article proved the existence of H<sup>1</sup> （R） ∩ L<sup>∞</sup> （R<sup>n</sup>） at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-（ij）(a<sub>ij</sub>（x,u）D<sub>j</sub>u) +1/2a<sub>iju</sub>（x,u）D<sub>i</sub>uD<sub>j</sub>u — q（x）|u|<sup>σ</sup>u = λu0≠u∈H<sup>1</sup>（R<sup>n</sup>） ,0【σ【 4/n,n≥3,x∈ R<sup>n</sup>Meanwhile the article studied the conditions of q（x） under which λ=0 was a bifurcation point for the nonlinear eigenvalue . Here a<sub>ij</sub> are not required to be bounded as u varies.展开更多
文摘The article proved the existence of H<sup>1</sup> （R） ∩ L<sup>∞</sup> （R<sup>n</sup>） at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-（ij）(a<sub>ij</sub>（x,u）D<sub>j</sub>u) +1/2a<sub>iju</sub>（x,u）D<sub>i</sub>uD<sub>j</sub>u — q（x）|u|<sup>σ</sup>u = λu0≠u∈H<sup>1</sup>（R<sup>n</sup>） ,0【σ【 4/n,n≥3,x∈ R<sup>n</sup>Meanwhile the article studied the conditions of q（x） under which λ=0 was a bifurcation point for the nonlinear eigenvalue . Here a<sub>ij</sub> are not required to be bounded as u varies.
