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

Ertem Türker, Zafer, Zafer Aäÿacä±K

Description

Consider the infinite interval nonlinear boundary value problem ( p ( t ) x ′ ) ′ + q ( t ) x = f ( t , x ) , t ≥ t 0 ≥ 0 , x ( t 0 ) = x 0 , x ( t ) = a v ( t ) + b u ( t ) + o ( r i ( t ) ) , t → ∞ , where 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.

Sujets

• Boundary value problem
• Singular
• Line (geometry)
• Principal

Informations

• Publié par: biomed
• Publié le: 01 janvier 2012
• Nombre de lectures: 7
• Langue: English

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