一类半正二阶Dirichlet边值问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2023.003

摘要/Abstract

摘要： 考察二阶半正问题{-u″(t)=λ(f(u(t))+a(t)),t∈(0,1),u(0)=u(1)=0正解的存在性,其中λ是正参数,a∈C(［0,1］,R), f∈C(［0,∞),［0,∞))。f满足超线性增长条件时,证得存在常数 λ^*>0,当0<λ<λ^*时,问题存在一个正解。主要结果的证明基于锥上的不动点定理。

关键词: 正解, 半正问题, Dirichlet边界条件, 不动点定理

Abstract: The existence of positive solutions for second-order semi-positone problem{-u″(t)=λ(f(u(t))+a(t)), t∈(0,1),u(0)=u(1)=0is studied, where λ is a positive parameter, a∈C(［0,1］, R), f∈C(［0,∞),［0,∞)). When f has a superlinear growth, we prove that there exists a constant λ^*>0 such that the problem has a positive solution for 0<λ<λ^*. The proof of the main results is based on a fixed point theorem in cones.

Key words: positive solution, semi-positone problem, Dirichlet boundary condition, fixed point theorem

中图分类号:

O175.8

李存丽. 一类半正二阶Dirichlet边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2024, 59(12): 96-101.

LI Cunli. Existence of positive solutions for a class of second-order semi-positone problems with Dirichlet boundary conditions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 96-101.

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