一类二阶半正问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2022.261

摘要/Abstract

摘要： 研究二阶半正问题{-u″(t)=λh(t)f(u(t)), t∈(0,1),αu(0)-b(u'(0))u'(0)=0, c(u(1))u(1)+δu'(1)=0正解的存在性,其中λ为正参数,α,δ>0为常数,b,c∈C(［0,∞),［0,∞)),h∈C(［0,1］,［0,∞)), f ∈C(［0,∞),R), f>-M(M>0)且f_∞:=lim_x→∞(f(x))/x=∞。主要定理的证明基于Krasnoselskii不动点定理。

关键词: 正解, 半正问题, 存在性, Krasnoselskii不动点定理

Abstract: The existence of positive solutions for the second order semipositone problem{-u″(t)=λh(t)f(u(t)), t∈(0,1),αu(0)-b(u'(0))u'(0)=0, c(u(1))u(1)+δu'(1)=0 is studied, where λ is a positive parameter,α,δ>0 are constants,b,c∈C(［0,∞),［0,∞)),h∈C(［0,1］,［0,∞)), f∈C(［0,∞),R), f >-M(M>0)and f_∞:=lim_x→∞(f(x))/x=∞。The proof of the main theorems is based on fixed point theorem of Krasnoselskii.

Key words: positive solution, semipositone problem, existence, Krasnoselskii fixed point theorem

中图分类号:

O175.8

石轩荣. 一类二阶半正问题正解的存在性[J]. 《山东大学学报(理学版)》, 2023, 58(4): 89-96.

SHI Xuan-rong. Existence of positive solutions for a class of second order semipositone problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 89-96.

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