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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.

34B18Positive solutions of nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
34B16Singular nonlinear boundary value problems for ODE