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Positive solutions for singular second order Neumann boundary value problems via a cone fixed point theorem. (English) Zbl 1167.34313
Summary: We consider the existence of positive solutions for the singular second order Neumann boundary value problem $$\cases x^n+k^2x=f(t)g(t,x),\quad 0<t<1,\\ x'(0)=x'(1)=0;\endcases$$ where $k\in (0,\frac\pi2)$ source is a constant, $g(t,x)$ is monotone locally with respect to $x$ and $f(t)$, $g(t,x)$ may be singular at $t=0$, $t=1$ and $x=0$.

##### MSC:
 34B18 Positive solutions of nonlinear boundary value problems for ODE 34B16 Singular nonlinear boundary value problems for ODE 47N20 Applications of operator theory to differential and integral equations
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##### References:
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