Electron. J. Diff. Eqns., Vol. 2003(2003), No. 89, pp. 1-12.

Positive solutions of boundary-value problems for 2m-order differential equations

Yuji Liu & Weigao Ge

Abstract:
This article concerns the existence of positive solutions to the differential equation
$$ (-1)^m x^{(2m)}(t)=f(t,x(t),x'(t),\dots,x^{(m)}(t)), \quad 0 less than t less than \pi, $$
subject to boundary condition
$$ x^{(2i)}(0)=x^{(2i)}(\pi)=0, $$
or to the boundary condition
$$ x^{(2i)}(0)=x^{(2i+1)}(\pi)=0, $$
for $i=0,1,\dots,m-1$. Sufficient conditions for the existence of at least one positive solution of each boundary-value problem are established. Motivated by references [7,17,21], the emphasis in this paper is that $f$ depends on all higher-order derivatives.

Submitted June 23, 2003. Published September 4, 2003.
Math Subject Classifications: 34B18, 34B15, 34B27
Key Words: Higher-order differential equation, boundary-value problem, positive solution, fixed point theorem

Show me the PDF file (210K), TEX file, and other files for this article.

Yuji Liu
Department of Mathematics
Beijing Institute of Technology
Beijing, 100081, China
Department of Applied Mathematics
Hunan Institute of Technology, Hunan, 414000, China
email: liuyuji888@sohu.com
  Weigao Ge
Department of Applied Mathematics
Beijing Institute of Technology
Beijing, 100081, China

Return to the EJDE web page