JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 84-92.doi: 10.6040/j.issn.1671-9352.0.2019.781

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Existence of positive solutions for a class of semi-positive nonlinear elastic beam equation boundary value problems

WANG Jing-jing, LU Yan-qiong*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-06-01

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Abstract: By using the fixed point theorem of cone mapping, it obtains the existence and multiplicity of positive solutions for the semipositive nonlinear elastic beam equation boundary value problems{y(4)(x)+(k1+k2)y″(x)+k1k2y(x)=λf(x,y(x)), x∈［0,1］,y'(0)=y'(1)=y(0)=y(1)=0with Neumann boundary conditions, where 012≤(π2)/4, λ>0 is a parameter and f∈C(［0,1］×［0,∞),(-∞,∞)), with f(x,y)≥-X for some positive constant X.

Key words: semipositone Neumann boundary value problem, Greens function, positive solution, fixed point theorem

CLC Number: 

  • O175.8
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