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 $$\align -&x'' = p(t)f(t,y(t),x'(t)),\quad t\in (0,1),\\
-&y'' = q(t)g(t,x(t),y'(t)),\quad t\in (0,1),\\
& a_2y(0)-b_2y'(0)=y'(1)=0,\endalign$$ are established. The nonlinearities $f,g:[0,1]\times (0,\infty)\to [t,\infty)$ are allowed to be singular at $x'=0$ and $y'=0$. The functions $p,q\in C(0,1)$ 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.
|34B18||Positive solutions of nonlinear boundary value problems for ODE|
|34B15||Nonlinear boundary value problems for ODE|
|34B16||Singular nonlinear boundary value problems for ODE|