Existence of Positive Solutions for a Class of Nonlinear Second-Order Dirichlet Problem

Abstract:

~In this paper,~ we study the existence of positive solutions for a class of nonlinear second-order Dirichlet problem ~ $$ \left\{\begin{array}{ll} u''-\ a(t)u+f(t,u)= 0,~~\ \ \ 0< t< 1\\[2ex] \ u(0)=\ u(1)=0 \end{array} \right.\eqno $$\~where~$f:[0,1]\times R^{+}\rightarrow R^{+}$~is continuous,~$a:[0,1]\rightarrow R^{+}$~is continuous.~The proof of the main results is based on the fixed-point theorem of cone expansion-compression.