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In this paper, we prove existence results for the singular problem $ (-1)^{n-p}(Phi_m x^{(n-1)})' $ $ (t)=mu f(t, x(t), ldots, x^{(n-1)}(t)), $ for $ 0<1$, $x^{(i)}(0)=0 $, $ i=0, 1, ldots, p-1 $, $ x^{(i)}(1)=0$, $i=p $, $ p+1, ldots, n-1 $, $ max{x(t):tin [0, 1]}=A $. The paper presents conditions which guarantee that for any $ A>0 $ there exists $ mu_A>0 $ such that the above problem with $ mu=mu_{A} $ has a solution $ xin C^{n-1}([0, 1]) $ with $ Phi_m(x^{(n-1)})in AC([0, 1]) $ which is positive on $ (0, 1) $. Here the positive Carath'edory function $ f $ may be singular at the zero value of all its phase variables. Proofs are based on the Leray-Schauder degree and Vitali's convergence theorem

Singular right focal boundary value problem with given maximal values