BOUNDED AND UNBOUNDED POSITIVE SOLUTIONS FOR SINGULAR φ-LAPLACIANS COUPLED SYSTEM ON THE HALF-LINE WITH FIRST-ORDER DERIVATIVE DEPENDENCE

In this paper we prove by means of expansion and compression of a cone principle, the existence of a positive solution to the second order boundary value problem {-(phi(1)(u'))' (t) = a(1)(t)f(1)(t,u(t), v(t), u'(t), v'(t)) t > 0, -(phi(2)(v'))' (t) = a(2)(t)f(2)(t,u(t), v(t), u'(t), v'(t)) t > 0, u(0) = v(0) = (t ->+infinity)lim u'(t) = 0, (t ->+infinity)lim v'(t) = 0, where for i = 1,2, phi(i) : R -> R is an increasing homeomorphism such that phi(i)(0) = 0, a(i) is a measurable function with a(i)(t) > 0 a.e. t in some interval of (0,+infinity) and the nonlinearity f(i) : R+ x(0,+infinity)(4) -> R+ is continuous, and may exhibit singular at u+v= 0 and u' + v' = 0.