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Positive solutions for boundary-value problems with integral boundary conditions on infinite intervals. (English) Zbl 1255.34028

Summary: We consider the existence of positive solutions for the class of boundary value problems with integral boundary conditions on infinite intervals

(φ p (x ' (t))) ' +ϕ(t)f(t,x(t),x ' (t))=0,0<t<+,x(0)= 0 + g(s)x ' (s)ds,lim t+ x ' (t)=0,

where φ 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. An example is presented.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
34B40Boundary value problems for ODE on infinite intervals