JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 82-88.doi: 10.6040/j.issn.1671-9352.0.2022.222

Previous Articles    

Existence of positive solutions for a class of semipositone second order Neumann boundary value problems

LEI Xiang-bing   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-03-27

PDF (PC)

158

Abstract: This paper considers the existence of positive solutions of second order Neumann boundary value problems{u″(t)+a(t)u(t)=λf(t,u(t)), 0where λ is a positive parameter, a∈C［0,1］ and 0π2)/4, f∈C(［0,1］×R+,R)and f(t,0)<0. The proof of that there exists a positive constant λ0 such that the problem has one positive solution for 0<λ<λ0. The proof of the main results is based on topological degree theory.

Key words: Neumann boundary value problem, positive solution, semipositone, topological degree

CLC Number: 

  • O175.8
[1] JIANG Daqing, LIU Huizhao. Existence of positive solution to second order Neumann boundary vaule problems[J]. Journal of Mathematical Research and Exposition, 2000, 20(3):360-364.
[2] SUN Jianping, LI Wantong. Multiple positive solution to second order Neumann boundary value problems[J]. Applied Mathematics and Computation, 2003, 146(1):187-194.
[3] SUN Jianping, LI Wantong, CHENG Suisun. Three positive solution to second-order Neumann boundary value problems[J]. Applied Mathematics Letters, 2004, 17(9):1079-1084.
[4] 姚庆六. 非线性变系数Neumann边值问题的正解[J]. 山东大学学报(理学版), 2007, 42(12):10-14. YAO Qingliu. Positive solutions of nonlinear second-order Neumann boundary value problems with a variable coefficient[J]. Journal of Shangdong University(Natural Science), 2007, 42(12):10-14.
[5] CHU Jifeng, SUN Yigang, CHEN Hao. Positive solution of Neumann problens with singularities[J]. Journal of Mathematical Analysis and Applications, 2008, 337(2):1267-1272.
[6] SUN Yan, CHO Yeolje, O'REGAN D. Positive solution for singular second order Neumann boundary value problems via a cone fixed point theorem[J]. Applied Mathematics and Computation, 2009, 210(1):80-86.
[7] LI Xiaoyue, JIANG Daqing. Optimal existence theory for single and multiple positive solutions to second order Neumann boundary vaule problems[J]. Indian Journal of Pure and Applied Mathematics, 2004, 35(5):573-586.
[8] 闫东明. 变系数二阶Neumann边值问题正解的存在性[J]. 高校应用数学学报(A辑), 2013, 28(4):477-487. YAN Dongming. Existence of positive solutions to second order Neumann boundary value problems[J]. Journal of Applied Mathematics in Universities(Series A), 2013, 28(4):477-487.
[9] BENSEDIK A, BOUCHEKIF M. Symmetry and uniqueness of positive solutions for Neumann boundary value problem[J]. Applied Mathematics Letters, 2007, 20(4):419-426.
[10] LI Zhilong. Existence of positive solution of superlinear second-order Neumann boundary value problems[J]. Nonlinear Analysis, 2010, 72(6):3216-3221.
[11] ZEIDLER E. Nonlinear functional analysis and its applications[M]. New York: Springer-Verlag, 1985.
[12] 郭大均,孙经先. 非线性积分方程[M]. 济南:山东科学技术出版社, 1987. GUO Dajun, SUN Jingxian. Nonlinear integral equation[M]. Jinan: Shandong Science and Technology Press, 1987.
[1] SUN Xiao-yue. Multiplicity of positive solutions for elastic beam equations under inhomogeneous boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 65-73.
[2] XU Jing, GAO Hong-liang. Number of positive solutions for mean curvature problem with convex-concave nonlinearity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 74-81.
[3] HAN Zhuo-ru, LI Shan-bing. Positive solutions of predator-prey model with spatial heterogeneity and hunting cooperation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(7): 35-42.
[4] YANG Li-juan. Existence of positive solutions for a class of fourth-order boundary value problems with parameter [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(9): 35-41.
[5] LIU Meng-xue, LI Jie-mei, YAO Yan-yan. Multiplicity of positive solutions for fourth-order boundary value problems with nonlinear boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 84-91.
[6] SU Xiao-xiao, ZHANG Ya-li. Existence of positive solutions for periodic boundary value problems of secondorder damped difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 56-63.
[7] YANG Xiao-mei, LU Yan-qiong, WANG Rui. Ambrosetti-Prodi type results of the second-order discrete Neumann boundary value problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 64-74.
[8] ZHANG Ya-li. Global structure of the positive solution for a class of fourth-order boundary value problems with first derivative [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 102-110.
[9] WANG Jing-jing, LU Yan-qiong. Existence of positive solutions for a class of semi-positive nonlinear elastic beam equation boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 84-92.
[10] WANG Jing-jing, LU Yan-qiong. Existence of optimal positive solutions for Neumann boundary value problems of second order differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 113-120.
[11] ZHAO Jiao. Global structure of the set of positive solutions for a class of nonlinear third-order boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 104-110.
[12] . Uniqueness of positive solutions of singular p-biharmonic equations with Hardy terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 75-80.
[13] MA Man-tang. Existence of positive solutions for a class of periodic boundary value problems of nonlinear second-order systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 88-95.
[14] SU Xiao-xiao. Existence of positive solutions for periodic boundary conditions of singular second-order damped difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 38-45.
[15] HE Yan-qin, HAN Xiao-ling. Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 32-37.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd