Existence of solutions for a class of nonlinear boundary value problems on half-line
Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey
Boundary Value Problems 2012, 2012:43 doi:10.1186/1687-2770-2012-43Published: 16 April 2012
Consider the infinite interval nonlinear boundary value problem
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 ∈ (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.