The existence of three positive solutions for some nonlinear boundary value problems on the half-line

Abstract

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line $$(\varphi(u^\prime))^\prime + a(t)f(t, u(t)) = 0, \quad 0 < t <+\infty,$$ $$u(0) = \sum_{i=1}^{m-2} \alpha_iu(\xi_i), \quad u^\prime(\infty) = 0,$$ where \({\varphi:}R {\rightarrow}R\) is the increasing homeomorphism and positive homomorphism and \(\varphi(0) =0\). We show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term by using the five functionals fixed-point theorem.