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Existence and iteration of \(n\) symmetric positive solutions for a singular two-point boundary value problem. (English) Zbl 1062.34024

Summary: Let \(n\) be an arbitrary natural number. We consider the existence of \(n\) symmetric positive solutions and establish a corresponding iterative scheme for the two-point boundary value problem \[ w''(t)+h(t)f \bigl(w(t)\bigr)=0\;0<t<1,\quad \alpha w(0)-\beta w'(0)=0,\;\alpha w(1) +\beta w'(1)=0. \] The main tool is the monotone iterative technique. Here, the coefficient \(h(t)\) is symmetric on \((0,1)\) and may be singular at both end-points \(t=0\) and \(t=1\).

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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