Positive Solutions Of Second-order Problem With Dependence On Derivative In Nonlinearity Under Stieltjes Integral Boundary Condition

In this thesis,we investigate the existence of positive solutions of the second-order nonlinear differential equations of the form-u"{t)=f(t,u(t),u'(t)),t?[0,1],where f:[0,1]× R+×R+? R+is continuous.Its boundary conditions respectively are u(0)=a[u],u'(1)=0,u(0)??[u],u'(1)=?[u],Where ?[u],?[u]are linear functional given by Stieltjes integrals.Some inequality conditions on nonlinearity f are presented and allow that f(t,x1,x2)has superlinear or subl inear growth in x1,x2.Some inequality conditions on constructing linear operators' spectral radius are also presented.These equality conditions together guarantee the existence of positive solutions to the boundary problem.Our discussion is based on the fixed point index theory of completely continuous operators in cones.We also give some examples under integral and multi-point boundary conditions with sign-changing coefficients respectively illustrate application of the theorems.