Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POSITIVE PSEUDO-SYMMETRIC SOLUTIONS FOR THREE-POINT BOUNDARY VALUE PROBLEMS WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE

  • Guo, Yanping (College of Sciences, Hebei University of Science and Technology) ;
  • Han, Xiaohu (Hebei Administration Institute) ;
  • Wei, Wenying (College of Sciences, Hebei University of Science and Technology)
  • Received : 2009.11.20
  • Accepted : 2009.12.14
  • Published : 2010.09.30
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Abstract

In this paper, a new fixed point theorem in cone is applied to obtain the existence of at least one positive pseudo-symmetric solution for the second order three-point boundary value problem {x" + f(t, x, x')=0, t $\in$ (0, 1), x(0)=0, x(1)=x($\eta$), where f is nonnegative continuous function; ${\eta}\;{\in}$ (0, 1) and f(t, u, v) = f(1+$\eta$-t, u, -v).

Keywords

References

  1. R.Y.Ma, Positive solutions of a nonlinear three-point boundary value problems, Electronic Journal of Differential Equations, 34(1999), 1-8.
  2. R.Y.Ma, Existence theorems for a second order m-point boundary value problems, J. Math. Anal. Appl. 211(1997), 545-555. https://doi.org/10.1006/jmaa.1997.5416
  3. R.Y.Ma, Positive solution of three-point boundary value problems, Appl. Math. Lett. 14(2001), 1-5. https://doi.org/10.1016/S0893-9659(00)00102-6
  4. R.Y.Ma, Existence of solutions of nonlinear m-point boundary value problem, J. Math. Anal. Appl. 256(2001), 556-567. https://doi.org/10.1006/jmaa.2000.7320
  5. Y.P.Guo, W.G.Ge, Y.Gao, Twin positive solutions for higher order m-point boundary value problems with sign changing nonlinearities, Applied Mathematics and Computation, 146(2003), 299-311. https://doi.org/10.1016/S0096-3003(02)00542-8
  6. Y.P.Guo, J.W.Tian, Two positive solutions for second-order quasilinear differential equation boundary value problems with sign changing nonlinearities, Journal of computational and Applied Mathematics, 169(2004), 345-357. https://doi.org/10.1016/j.cam.2003.12.029
  7. Paul. W. Eloe, Bashir Ahmad, Positive solutions of a nonlinear nth boundary value problems with nonlocal conditions, Applied Mathematics Letters, 18(2005), 521-527. https://doi.org/10.1016/j.aml.2004.05.009
  8. Y.P.Guo,W.G.Ge, Positive solutings for three-point boundary value problems with dependence on the first order derivative,J. Math. Anal. Appl. 290(2004), 291-301. https://doi.org/10.1016/j.jmaa.2003.09.061
  9. B.Sun,W.G.Ge, Successive itration and positive pseudo-symmetric solutions for a three-point second-order p-Laplacian boundary value problem, Applied Mathematics and Computation, 188(2007), 1772-1779. https://doi.org/10.1016/j.amc.2006.11.040
  10. Avery and Henderson, Existence of Three Positive Pseudo-Symmetric Solutions for a One Dimensional p-Laplacian, Journal of Mathematical Analysis and Applications, Volume 277 (2003), 395-404. https://doi.org/10.1016/S0022-247X(02)00308-6