Journal of Northeastern University Natural Science ›› 2020, Vol. 41 ›› Issue (4): 604-608.DOI: 10.12068/j.issn.1005-3026.2020.04.026

• Mathematics • Previous Articles    

Positive Solutions of Second-Order Boundary Value Problems with Sign-Changing Green’s Function

ZHANG Guo-wei, QU Xue-bing   

  1. School of Sciences, Northeastern University, Shenyang 110819, China.
  • Received:2019-09-26 Revised:2019-09-26 Online:2020-04-15 Published:2020-04-17
  • Contact: QU Xue-bing
  • About author:-
  • Supported by:
    -

Abstract: The existence of positive solutions for a class of second-order boundary value problems with a sign-changing Green’s function was studied, and the sign-changing Green’s function was caused by different values of coefficients in boundary value conditions, which is different from that the change of the coefficient of the first order of the unknown function usually leads to the change of the Green’s function. When there is no non-negative limitation of nonlinear term, the existence of positive solutions for second-order boundary value problems was proved by giving constraints to the positive and negative parts of Green’s function. The validity of the theoretical results was illustrated by two concrete examples, in which the coefficients of boundary value condition include both positive and negative cases. In addition, two different boundary conditions were explained.

Key words: positive solution, sign-changing Green’s function, second-order boundary value problem, completely continuous operator, Leray-Schauder fixed point theorem

CLC Number: