Positivity

, Volume 12, Issue 3, pp 555–569

Positive solutions for second-order superlinear repulsive singular Neumann boundary value problems

  • Jifeng Chu
  • Xiaoning Lin
  • Daqing Jiang
  • Donal O’Regan
  • Ravi P. Agarwal
Article

DOI: 10.1007/s11117-007-2144-0

Cite this article as:
Chu, J., Lin, X., Jiang, D. et al. Positivity (2008) 12: 555. doi:10.1007/s11117-007-2144-0

Abstract

In this paper we establish the multiplicity of positive solutions to second-order superlinear repulsive singular Neumann boundary value problems. It is proved that such a problem has at least two positive solutions under reasonable conditions. Our nonlinearity may be repulsive singular in its dependent variable and superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.

Mathematics Subject Classification (2000)

34B15

Keywords

Superlinearrepulsive singularNeumann boundary value problemspositive solutionsleray-Schauder alternativefixed point theorem in cones

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Jifeng Chu
    • 1
  • Xiaoning Lin
    • 2
  • Daqing Jiang
    • 2
  • Donal O’Regan
    • 3
  • Ravi P. Agarwal
    • 4
  1. 1.College of ScienceHohai UniversityNanjingChina
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchunChina
  3. 3.Department of MathematicsNational University of IrelandGalwayIreland
  4. 4.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA