Let \(k\) be a positive integer, \(M_0\) and \(M_1\) subsets of \(\{0,1,\dots,k-1\}\) such that the sum of their cardinalities is \(k\). Suppose that the solution \(u=u(x)\) of the boundary value problem \(u^{(k)}=f\) in \((0,1)\), \(u^{(i)}=0\) for \(i\in M_0\), \(u^{(j)}(1)=0\) for \(j\in M_1\) with \(f\) not changing sign in \((0,1)\) can be expressed uniquely in the form \[ u(x)= \int^x_0 K_1(x,t)f(t)dt+ \int^1_x K_2(x,t)f(t)dt. \] The author asks whether there exist positive constants \(C_1\), \(C_2\), and nonnegative integers \(\alpha_1\), \(\alpha_2\), \(\beta_1\), \(\beta_2\), \(\gamma_1\), \(\gamma_2\), \(\delta_1\), \(\delta_2\), such that \(c_1\leq{K_i(x,t)\over x^{\alpha_i}(1-x)^{\beta_i}t^{\gamma_i}(1-t)^{\delta_i}}\leq C_2\) for \(0