A third order boundary value problem on an unbounded domain

摘要

We consider the third order nonlinear differential equation(p(t)u' (t))" = f (t,u(t),u" (t)),a. e. in (0, ∞), satisfying the boundary conditions u(0) = u'(0) = 0, lim u(t) = αu(β). where α,β ∈ (0, ∞), f : [0, ∞) x R~3→ R is Caratheodory with respect to L_1 [0, ∞), p ∈ C~2(0, ∞) and p(t) > 0 for all t > 0. We obtain the existence of at least one solution using the Leray-Schauder Continuation Principle.