Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions

D. R. Dunninger; Haiyan Wang

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 2, page 155-165
  • ISSN: 0066-2216

Abstract

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We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.

How to cite

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D. R. Dunninger, and Haiyan Wang. "Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions." Annales Polonici Mathematici 69.2 (1998): 155-165. <http://eudml.org/doc/270231>.

@article{D1998,
abstract = {We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.},
author = {D. R. Dunninger, Haiyan Wang},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear boundary value problems; multiplicity of positive solutions; upper and lower solutions; degree theory; nonlinear differential equation; positive solution},
language = {eng},
number = {2},
pages = {155-165},
title = {Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions},
url = {http://eudml.org/doc/270231},
volume = {69},
year = {1998},
}

TY - JOUR
AU - D. R. Dunninger
AU - Haiyan Wang
TI - Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 2
SP - 155
EP - 165
AB - We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
LA - eng
KW - nonlinear boundary value problems; multiplicity of positive solutions; upper and lower solutions; degree theory; nonlinear differential equation; positive solution
UR - http://eudml.org/doc/270231
ER -

References

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  1. [1] H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. 21 (1971), 125-146. Zbl0219.35037
  2. [2] H. Amann, On the number of solutions of asymptotically superlinear two point boundary value problems, Arch. Rational Mech. Anal. 55 (1974), 207-213. Zbl0294.34008
  3. [3] D. S. Cohen, Generalized radiation cooling of a convex solid, J. Math. Anal. Appl. 35 (1971), 503-511. Zbl0218.35036
  4. [4] H. Dang, K. Schmidt and R. Shivaji, On the number of solutions of boundary value problems involving the p-Laplacian, Electron. J. Differential Equations 1 (1996), 1-9. 
  5. [5] D. R. Dunninger and H. Wang, Multiplicity of positive solutions for an elliptic system, preprint. Zbl0959.35051
  6. [6] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, FL, 1988. Zbl0661.47045
  7. [7] K. S. Ha and Y. Lee, Existence of multiple positive solutions of singular boundary value problems, Nonlinear Anal. 28 (1997), 1429-1438. Zbl0874.34016
  8. [8] S. S. Lin, Positive radial solutions and nonradial bifurcation for semilinear elliptic equations in annular domains, J. Differential Equations 86 (1990), 367-391. Zbl0734.35073

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