Throughout positive solutions of second-order nonlinear differential equations

Abstract

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations $$displaylines{ (a(t)x'(t))'+f(t,x(g(t)))=0,quad tgeq t_0cr (a(t)(x(t)-p(t)x(t-au))')'+f(t,x(g(t)))=0,quad tgeq t_0,. }$$ Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.

Keywords

• Nonlinear differential equations
• neutral term
• eventually positive solution
• throughout positive solution.