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Existence of solutions for a class of nonlinear boundary value problems on half-line

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2012-4-16
Ertem, Türker
Zafer, Ağacık
Consider the infinite interval nonlinear boundary value problem (p(t)x ) + q(t)x = f (t, x), t ≥ t0 ≥ 0, x(t0) = x0, x(t) = a v(t) + b u(t) + o(ri(t)), t → ∞, where u and v are principal and nonprincipal solutions of (p(t)x’)’ + q(t)x = 0, r1(t) = o (u(t)(v(t))μ ) and r2(t) = o(v(t)(u(t))μ ) for some μ Î (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.