Existence and uniqueness of positive solutions for a singular second-order integral boundary value problem
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 \textit{D. Wardowski} [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)]. Moreover, we present several examples illustrating our result.
scientific article; zbMATH DE number 7367446