In this paper N-dimensional singular, p-Laplace equations of the following form △pu:=N↑∑↑i=1Di(|Du|^p-2Diu)=f(|x|,u,|Du|u^-β,x∈R^N(N≥3) are considered, where p≥N,β〉0,and f:[0,∞)×[0,∞)...In this paper N-dimensional singular, p-Laplace equations of the following form △pu:=N↑∑↑i=1Di(|Du|^p-2Diu)=f(|x|,u,|Du|u^-β,x∈R^N(N≥3) are considered, where p≥N,β〉0,and f:[0,∞)×[0,∞)×[0,∞)is a continuous tunctlon. Some sufficient conditions are obtained for the existence of infinitely many radially positive entire solutions of the equation which are asymptotic to positive constant multiples of |x|^(p-N)/(p-1) for p〉N or log|x| for N-p as |x|→∞.展开更多
基金The work is supported by the National Natural Science Foundation of China (10271056)the Natural Science Foundation of Fujian Province (F00018).
文摘In this paper N-dimensional singular, p-Laplace equations of the following form △pu:=N↑∑↑i=1Di(|Du|^p-2Diu)=f(|x|,u,|Du|u^-β,x∈R^N(N≥3) are considered, where p≥N,β〉0,and f:[0,∞)×[0,∞)×[0,∞)is a continuous tunctlon. Some sufficient conditions are obtained for the existence of infinitely many radially positive entire solutions of the equation which are asymptotic to positive constant multiples of |x|^(p-N)/(p-1) for p〉N or log|x| for N-p as |x|→∞.