Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

EXISTENCE OF SOLUTIONS OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS FOR 2NTH-ORDER NONLINEAR DIFFERENTIAL EQUATION

  • Gao, Yongxin (College of Science of Civil Aviation University of China) ;
  • Wang, Renfei (College of Science of Civil Aviation University of China)
  • Published : 2009.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

Keywords

References

  1. L. K. Jackson and K. Schrader, Subfunction and third order differential inequalities, J. Differential Equation 8 (1970), 180-194. https://doi.org/10.1016/0022-0396(70)90044-6
  2. P. Hartman,Ordinary Differential Equations, Wiley,New York, 1964.
  3. G. A. KlasenDifferential inequalities and existence theorems for second and third order boundary value problems, J. Differential Equation 10 (1971), 529-537. https://doi.org/10.1016/0022-0396(71)90010-6
  4. Gao Yongxin, Existence of solutions of nonlinear two-point boundary value problems for 4nth-order nonlinear differential equation, J.Harbin Institute of Technology (New Series) 4 (2002), 424 - 428.
  5. Wang Jinzi, Existence of solutions of nonlinear two-point boundary value problems for third order nonlinear differential equations, Northeast Math.J. 7 (1991), 181-189.