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Existence and uniqueness of positive solutions for a singular second-order integral boundary value problem. (English) Zbl 1481.34031

Summary: In this work, we discuss the existence and uniqueness of positive solutions for the second order integral boundary value problem \[ \begin{cases} x''(t)+f(t,x(t),(Hx)(t))=0, \quad 0<t<1,\\ x(0)=0,\quad x(1)= \int_0^1a(s)x(s)ds, \end{cases} \] where the function \(f\) has a singularity at \(t_0=0\). Our main tool is a fixed point theorem of D. Wardowski [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)]. Moreover, we present several examples illustrating our result.

MSC:

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

Citations:

Zbl 1310.54074
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References:

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