Electron. J. Diff. Equ., Vol. 2012 (2012), No. 158, pp. 1-9.

Positive solutions for boundary-value problems with integral boundary conditions on infinite intervals

Changlong Yu, Jufang Wang, Yanping Guo, Huixian Wei

Abstract:
In this article, we consider the existence of positive solutions for a class of boundary value problems with integral boundary conditions on infinite intervals
$$\displaylines{
 (\varphi_{p}(x'(t)))'+\phi(t)f(t,x(t),x'(t))=0, \quad 0<t<+\infty,\cr
 x(0)=\int_0^{+\infty}g(s)x'(s)ds,\quad \lim_{t\to+\infty}x'(t)=0,
 }$$
where $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$. By applying the Avery-Peterson fixed point theorem in a cone, we obtain the existence of three positive solutions to the above boundary value problem and give an example at last.

Submitted July 5, 2012. Published September 18, 2012.
Math Subject Classifications: 34B18, 34B15.
Key Words: Cone; Avery-Peterson fixed point theorem; positive solution; integral boundary conditions; infinite interval.

Show me the PDF file (228 KB), TEX file, and other files for this article.

Changlong Yu
College of Sciences
Hebei University of Science and Technology
Shijiazhuang, 050018, China
email: changlongyu@126.com
  Jufang Wang
College of Sciences
Hebei University of Science and Technology
Shijiazhuang, 050018, China
email: wangjufang1981@126.com
  Yanping Guo
College of Sciences
Hebei University of Science and Technology
Shijiazhuang, 050018, China
  Huixian Wei
Department of Baise
Shijiazhuang Institute of Railway Technology
Shijiazhuang, 050041, China

Return to the EJDE web page