NONTRIVIAL SOLUTIONS OF SINGULAR SECOND ORDER THERE-POINT BOUNDARY VALUE PROBLEM AT RESONANCEN

Volume 1, Issue 1, pp 49-55 http://dx.doi.org/10.22436/jnsa.001.01.08

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Authors

XIAORONG WU - Department of Mathematics and Physics, Taizhou Teachers College, Taizhou, 225300, China.. FENG WANG - School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou, 213164, China..

Abstract

The singular second order three-point boundary value problem at resonance \[ \begin{cases} x''(t) = f(t, x(t)),\,\,\,\,\, 0 < t < 1,\\ x'(0) = 0, x(\eta) = x(1), \end{cases} \] are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where \(\eta\in (0, 1)\) is a constant, \(f\) is allowed to be singular at both \(t = 0\) and \(t = 1\). The existence results of nontrivial solutions are given by means of the topological degree theory.

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Keywords

• Singular
• Nontrivial solutions
• Boundary value problem
• Topology degree
• Resonance.

MSC

•  34B15
•  34B25

References

• [1] W. Feng, JRL. Webb , Solvability of a three-point nonlinear BVPs at resonance, Nonlinear Anal. , 30 (1997), 3227–3238


• [2] R. Ma , Multiplicity results for a three-point boundary value problems at resonance, Nonlinear Anal. , 53 (2003), 777–789
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] Z. Bai, W. Li, W. Ge , Existence and multiplicity of solutions for four-point BVPs at resonance, Nonlinear Anal., 60 (2005), 1551–1562
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] X. Han , Positive solutions for a three-point boundary value problems at resonance, J. Math. Anal. Appl. , 336 (2007), 556–568
  • View Article
  • MathSciNet
  • Google Scholar


• [5] C. Bai, J. Fang, Existence of positive solutions for three-point boundary value problems at resonance, J. Math. Anal. Appl., 291 (2004), 538–549
  • View Article
  • MathSciNet
  • Google Scholar


• [6] G. Infante, M. Zima , Positive solutions of multi-point boundary value problems at resonance , Nonlinear Anal. , 69 (2008), 2458-2465
  • View Article
  • Google Scholar


• [7] J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, , Berlin (1979)
  • MathSciNet
  • Google Scholar


• [8] G. Zhang, J. Sun, Positive solutions of m-point boundary value problems, J. Math. Anal. Appl., 291 (2004), 406–418
  • View Article
  • Google Scholar


• [9] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego (1988)
  • MathSciNet


• [10] D. Guo, J. Sun, Nonlinear Integral Equations, Shandong Press of Science and Technology, Jinan, (in Chinese) (1987 )


• [11] Deimling Klaus, Nonlinear Functional Analysis, Springer-Verlag, New York (1985)