Open Access Research

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

Türker Ertem* and Ağacık Zafer

Author Affiliations

Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

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Boundary Value Problems 2012, 2012:43 doi:10.1186/1687-2770-2012-43

Published: 16 April 2012

Abstract

Consider the infinite interval nonlinear boundary value problem

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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.

Keywords:
Boundary value problem; singular; half-line; principal; nonprincipal