【摘要】 研究了以下非线性Dirichlet问题在一定条件下的弱正解的存在性 :-div(｜ u｜p- 2 u) +a(x)up- 1=h(x)uq+up - 1,x∈RN,u≥ 0 ,u 0 ,∫RN a(x)·｜u｜pdx <+∞ .其中 ,a :RN →R是连续非负函数 ,h :RN →R是某类可积函数 ,2≤ p <N且 p2 ≤N ,0 <q <p2 (p - 1)N- p - 1,p =NpN- p.从而在更弱的条件下将 p=2或次临界指数的情形推广到P_Laplacian及临界指数的情形 ,同时推广了a(x) =0时的某些结果 .更多还原

【Abstract】 This paper is concerned with the existence of the we ak positive solution of the following nonlinear Dirichlet problem on some conditio ns:- div (|u| p-2 u)+a(x)u p-1 =h(x)u q+u p *-1 ,x∈R N,u≥0,u0,∫ R N ?a(x)|u| p d x<+∞.Where a : R N →R is continuous and nonnegati ve, h : R N →R is some integrable function and 2 ≤ p<N, p 2≤ N, 0<q<p 2(p-1)N-p-1, p *=NpN-p . Some results as p =2 or sub_ critical exponent are generalized to P_Laplacian and critical exponent on weaker conditions, and some results as a(x) =0 are generalized too.更多还原