Multiplicity results for positive solutions of a coupled system of singular boundary value problems. (English) Zbl 1260.34039
Summary: Existence of multiple positive solutions for a coupled system of nonlinear two-point singular boundary value problems $$\align -x''(t) &= p(t) f(t,y(t), x'(t)),\quad t\in (0,1),\\ -y''(t) &= q(t) g(t, x(t), y'(t)),\quad t\in (0,1),\\ x(0) &= y(0)= x'(1)= y'(1)= 0,\endalign$$ is established. The nonlinearities $f,g: [0,1]\times[0,\infty)\times (0,\infty)\to [0,\infty)$ are allowed to be singular at $x'=0$ and $y'=0$ and the functions $p,q\in C(0,1)$ are positive on $(0,1)$. An example is also included to show the applicability of our result.
|34B18||Positive solutions of nonlinear boundary value problems for ODE|
|47N20||Applications of operator theory to differential and integral equations|
|34B16||Singular nonlinear boundary value problems for ODE|