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

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 $$displaylines{ (varphi_{p}(x'(t)))'+phi(t)f(t,x(t),x'(t))=0, quad 0<t<+infty,cr x(0)=int_0^{+infty}g(s)x'(s)ds,quad lim_{to+infty}x'(t)=0, }$$ 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.

Keywords

• Cone
• Avery-Peterson fixed point theorem
• positive solution
• integral boundary conditions
• infinite interval