SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

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

For all author emails, please log on.

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

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/43/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/43/mathml/M1">View MathML</a>

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