Existence and asymptotic behavior of solutions for a class of Kirchhoff-type equations on the real half-line

This paper is concerned with the following Kirchhoff-type equation:\/ -(a+b∫_0^(+∞)|u^' |^2 dx) u''+p(x)u=q(x)f(u),x∈(0,+∞)), where a>0,b≥0 are constants, \(f∈C(R), p∈C(R^+,R_*^+) and q∈L^1 (0,∞)). Firstly, by using the Ekeland's variational principle, we show the existence of solutions to the above equation in the case where f is a sublinear function. Then, we establish the existence of solutions in the case where f is a superlinear function by using the Mountain pass theorem. Moreover, we discuss the asymptotic behavior of the obtained solutions in both cases with respect to the parameter b. Some recent results are complemented and extended.