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The boundary value problem is considered provided that f : [0, +∞) → [0, +∞) is Lipschitzian and
is continuous and Lipschitzian in x and x′. We assume that f is bounded by two linear functions kx and lx, where k > l > 0, and h is bounded. We find the conditions on (λ, µ) which guarantee the existence of a solution to the problem. These conditions are of geometrical nature.
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