JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (03): 62-66.doi: 10.6040/j.issn.1671-9352.0.2014.326

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The Ambrosetti-Prodi type results of the nonlinear second-order Neumann boundary value problem

MA Lu-yi   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2014-07-15 Revised:2014-11-07 Online:2015-03-20 Published:2015-03-13

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Abstract: We study the relationship between s and the number of solutions of the second-order Neumann boundary value problem 

where f∈C([0,1]×R2,R), s∈R is a parameter. By using the method of the upper and lower solutions and topological degree techniques, we obtain that the problem has no solution, at least one solution and at least two solutions, when s<s1, s=s1, s>s1, respectively.

Key words: topological degree, upper and lower solutions, Ambrosetti-Prodi problem

CLC Number: 

  • O175.8
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