摘要
本文在假设条件(H_1)和(H_2)之下,建立了奇异的非线性两点边值问题(1),(2)_0的正解的存在性与唯一性。
In this paper the existence and uniqueness of positive solutions for the singular nonlinear two point boundary value problems (1), (2)_0 is established under the following hypotheses:(H_1) M, (s), i=1, 2, …, n, is strictly increasing, locally absolutely continuous function defined on=[0, +∞) with M_i(0)=0, and its inverse function is denoted as N_i(t).(H_2)F_i(t, x_1, …, x_i), i=1, 2, …, n, is such a nonnegative function defined in [A, B] ×R_+×…×that(1) F_i(t, x_1, …, x_i) is integrable on [A, B] for each fixed (x_1, x_2, …, x_i)∈R_-×…×,(2) F_i(t, x_1, …, x_i) is continuous and decreasing in x_1∈R_-for almost all t∈ [A, B] and all (x_2, …, x_i)∈×…×, and(3) F_i(t, x_1, …, x_i) is continuous and increasing in x_k∈for almost all t∈[A, B] and all (x_1, …, x_(k-1), x_(k+1), …, x_i)∈R_+ … k=2, … .i.
出处
《吉林大学自然科学学报》
CSCD
1992年第4期30-32,共3页
Acta Scientiarum Naturalium Universitatis Jilinensis
关键词
两点边值问题
微分方程组
非线性
two point boundary value problem
positive solution
existence
uniqueness
