JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 50-55.doi: 10.6040/j.issn.1671-9352.0.2024.008

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Existence of positive solutions of a second-order Neumann boundary value problem with derivative term

WANG Liyuan, MA Ruyun*   

  1. School of Mathematics and Statistics, Xidian University, Xian 710126, Shaanxi, China
  • Published:2025-05-19

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Abstract: This paper studies the existence of positive solutions of a second-order Neumann boundary value problem with derivative term{-u″+k2u=f(t,u,u'), 0k>0 is a constant, f:［0,1］×［0,∞)×R→［0,∞)is a continuous function. Under superlinearity condition and Nagumo-type condition on f, the problem has at least one positive solution. The proof of the main results is based on fixed-point index.

Key words: Neumann problem, positive solution, fixed-point index, existence

CLC Number: 

  • O175.8
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