Consider the infinite interval nonlinear boundary value problemwhere u and v are principal and nonprincipal solutions of (p(t)x')' + q(t)x = 0, r 1 (t) = o (u(t)(v(t)) μ ) and r 2 (t) = o(v(t)(u(t)) μ ) for some μ (0, 1), and a and b are arbitrary but fixed real numbers. Sufficient conditions are given for the existence of a unique solution of the above problem for i = 1, 2. An example is given to illustrate one of the main results. Mathematics Subject Classication 2011: 34D05.
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