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.

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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

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