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Positive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order Differential Equations

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Some existence theorems of the positive solutions and the multiple positive solutions for singular and nonsingular systems of nonlinear fourth-order boundary value problems are proved by using topological degree theory and cone theory.



  1. 1.

    Gupta CP: Existence and uniqueness theorems for the bending of an elastic beam equation. Applicable Analysis 1988,26(4):289-304. 10.1080/00036818808839715

  2. 2.

    Gupta CP: Existence and uniqueness results for the bending of an elastic beam equation at resonance. Journal of Mathematical Analysis and Applications 1988,135(1):208-225. 10.1016/0022-247X(88)90149-7

  3. 3.

    Agarwal RP: On fourth order boundary value problems arising in beam analysis. Differential Integral Equations 1989,2(1):91-110.

  4. 4.

    O'Regan D: Solvability of some fourth (and higher) order singular boundary value problems. Journal of Mathematical Analysis and Applications 1991,161(1):78-116. 10.1016/0022-247X(91)90363-5

  5. 5.

    Yang YS: Fourth-order two-point boundary value problems. Proceedings of the American Mathematical Society 1988,104(1):175-180. 10.1090/S0002-9939-1988-0958062-3

  6. 6.

    Ma R, Wang H: On the existence of positive solutions of fourth-order ordinary differential equations. Applicable Analysis 1995,59(1–4):225-231.

  7. 7.

    Wei ZL, Zhang ZT: A necessary and sufficient condition for the existence of positive solutions of singular superlinear boundary value problems. Acta Mathematica Sinica 2005,48(1):25-34.

  8. 8.

    Wei ZL: Positive solutions to singular boundary value problems for a class of fourth-order sublinear differential equations. Acta Mathematica Sinica 2005,48(4):727-738.

  9. 9.

    Li YX: Existence and multiplicity of positive solutions for fourth-order boundary value problems. Acta Mathematicae Applicatae Sinica 2003,26(1):109-116.

  10. 10.

    Zhou YM: Positive solutions to fourth-order nonlinear eigenvalue problems. Journal of Systems Science and Mathematical Sciences 2004,24(4):433-442.

  11. 11.

    Guo DJ: Nonlinear Functional Analysis. Science and Technology Press, Jinan, Shandong, China; 1985.

  12. 12.

    Guo DJ, Lakshmikantham V: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering. Volume 5. Academic Press, Boston, Mass, USA; 1988:viii+275.

  13. 13.

    Cheng JG: Nonlinear singular boundary value problems. Acta Mathematicae Applicatae Sinica 2000,23(1):122-129.

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Correspondence to Shengli Xie.

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  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Existence Theorem