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Existence of positive solutions to a system of singular boundary value problems. (English) Zbl 1215.34029

Summary: Existence results for positive solutions of a coupled system of nonlinear singular two point boundary value problems of the type

-x '' =p(t)f(t,y(t),x ' (t)),t(0,1),-y '' =q(t)g(t,x(t),y ' (t)),t(0,1),a 1 x(0)-b 1 x ' (0)=x ' (1)=0,a 2 y(0)-b 2 y ' (0)=y ' (1)=0,

are established. The nonlinearities f,g:[0,1]×(0,)[t,) are allowed to be singular at x ' =0 and y ' =0. The functions p,qC(0,1) are positive on (0,1) and the constants a i ,b i >0 (i=1,2). An example is included to show the applicability of our result.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE